9046 Number Patterns Geometric Infinite Series

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| By Anthony Nunan
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Anthony Nunan
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Quizzes Created: 132 | Total Attempts: 47,368
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  • 1/95 Questions
    A baby kangaroo is grazing in a paddock 20 metres outside the National Park. He sees a ute full of noisy teenagers driving his way, and decides that the park might be safer than a farmers paddock. He bounds toward the fence, his first leap taking him 5 metres. Each successive leap is 20% less than the previous leap. How many leaps will it take the kangaroo to reach safety? - ProProfs

    A baby kangaroo is grazing in a paddock 20 metres outside the National Park. He sees a ute full of noisy teenagers driving his way, and decides that the park might be safer than a farmers paddock. He bounds toward the fence, his first leap taking him 5 metres. Each successive leap is 20% less than the previous leap. How many leaps will it take the kangaroo to reach safety?

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9046 Number Patterns Geometric Infinite Series - Quiz
About This Quiz

Explore the application of geometric series in real-world scenarios through this engaging quiz titled '9046 Number Patterns Geometric Infinite Series'. Assess your understanding of mathematical concepts as you solve problems involving bouncing superballs, bounding kangaroos, spreading paint stains, and skipping stones.

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  • 2. 
    I’m standing by a lake, skipping stones. My first skip is 5 metres, and each successive skip is 30% less. What is the total distance (to the nearest whole number) my stone will travel before it stops skipping? - ProProfs

    I’m standing by a lake, skipping stones. My first skip is 5 metres, and each successive skip is 30% less. What is the total distance (to the nearest whole number) my stone will travel before it stops skipping?

    Explanation
    Use ar, where R is converted to r. Find the infinite series

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  • 3. 
    From the sequence above, can an infinite geometric series be calculated? - ProProfs

    From the sequence above, can an infinite geometric series be calculated?

    • Yes, it is geometric and it is converging

    • No, it is geometric but it diverges

    • No, it's not even geometric

    Correct Answer
    A. No, it's not even geometric
    Explanation
    The given sequence is not even geometric because a geometric sequence is one in which each term is obtained by multiplying the previous term by a constant. In this case, there is no common ratio between the terms, so it cannot be considered a geometric series.

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  • 4. 
    From the sequence above, can an infinite geometric series be calculated? - ProProfs

    From the sequence above, can an infinite geometric series be calculated?

    • Yes, it is geometric and it is converging

    • No, it is geometric but it diverges

    • No, it's not even geometric

    Correct Answer
    A. No, it's not even geometric
    Explanation
    The given sequence is not even geometric because a geometric sequence is one in which each term is obtained by multiplying the previous term by a constant ratio. In this sequence, there is no constant ratio between the terms, so it cannot be considered geometric. Therefore, an infinite geometric series cannot be calculated from this sequence.

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  • 5. 
    From the sequence above, can an infinite geometric series be calculated? - ProProfs

    From the sequence above, can an infinite geometric series be calculated?

    • Yes, it is geometric and it is converging

    • No, it is geometric but it diverges

    • No, it's not even geometric

    Correct Answer
    A. No, it's not even geometric
    Explanation
    The given sequence is not even geometric because a geometric sequence is one in which each term is obtained by multiplying the previous term by a constant ratio. However, in the given sequence, there is no constant ratio between the terms. Therefore, an infinite geometric series cannot be calculated from this sequence.

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  • 6. 
    From the sequence above, can an infinite geometric series be calculated? - ProProfs

    From the sequence above, can an infinite geometric series be calculated?

    • Yes, it is geometric and it is converging

    • No, it is geometric but it diverges

    • No, it's not even geometric

    Correct Answer
    A. No, it's not even geometric
  • 7. 
    From the sequence above, can an infinite geometric series be calculated? - ProProfs

    From the sequence above, can an infinite geometric series be calculated?

    • Yes, it is geometric and it is converging

    • No, it is geometric but it diverges

    • No, it's not even geometric

    Correct Answer
    A. No, it's not even geometric
    Explanation
    The given sequence cannot be considered geometric because a geometric sequence must have a common ratio between consecutive terms. In this case, there is no common ratio between the terms, so it cannot be considered geometric. Therefore, an infinite geometric series cannot be calculated.

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  • 8. 
    From the sequence above, can an infinite geometric series be calculated? - ProProfs

    From the sequence above, can an infinite geometric series be calculated?

    • Yes, it is geometric and it is converging

    • No, it is geometric but it diverges

    • No, it's not even geometric

    Correct Answer
    A. No, it's not even geometric
    Explanation
    The given sequence does not have a common ratio between its terms, which is a requirement for a sequence to be geometric. Therefore, it cannot be considered as a geometric series.

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  • 9. 
    From the sum of the sequence above, can an infinite geometric series be calculated? - ProProfs

    From the sum of the sequence above, can an infinite geometric series be calculated?

    • Yes, it is geometric and it is converging

    • No, it is geometric but it diverges

    • No, it's not even geometric

    Correct Answer
    A. No, it is geometric but it diverges
    Explanation
    The question is asking whether an infinite geometric series can be calculated from the given sequence. The answer is no, even though the sequence is geometric, it diverges. This means that the terms in the sequence do not approach a finite value as the sequence progresses, making it impossible to calculate the sum of an infinite geometric series.

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  • 10. 
    From the sum of the sequence above, can an infinite geometric series be calculated? - ProProfs

    From the sum of the sequence above, can an infinite geometric series be calculated?

    • Yes, it is geometric and it is converging

    • No, it is geometric but it diverges

    • No, it's not even geometric

    Correct Answer
    A. No, it is geometric but it diverges
    Explanation
    The sequence mentioned in the question is geometric, meaning that each term is obtained by multiplying the previous term by a constant ratio. However, the fact that it diverges means that the terms of the sequence do not approach a finite value as the number of terms increases. Therefore, an infinite geometric series cannot be calculated from this sequence.

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  • 11. 
    From the sum of the sequence above, can an infinite geometric series be calculated? - ProProfs

    From the sum of the sequence above, can an infinite geometric series be calculated?

    • Yes, it is geometric and it is converging

    • No, it is geometric but it diverges

    • No, it's not even geometric

    Correct Answer
    A. No, it is geometric but it diverges
    Explanation
    The given sequence is geometric because each term is obtained by multiplying the previous term by a constant ratio. However, the sequence diverges because the terms do not approach a finite value as the number of terms increases. Therefore, an infinite geometric series cannot be calculated from this sequence.

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  • 12. 
    From the values given above, can an infinite geometric series be calculated? - ProProfs

    From the values given above, can an infinite geometric series be calculated?

    • Yes, it is geometric and it is converging

    • No, it is geometric but it diverges

    • No, it's not even geometric

    Correct Answer
    A. No, it is geometric but it diverges
    Explanation
    The correct answer is No, it is geometric but it diverges. This means that although the series is geometric, it does not converge to a specific value. In a geometric series, each term is obtained by multiplying the previous term by a constant ratio. However, in this case, the terms do not approach a finite value as the series progresses, indicating that it diverges.

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  • 13. 
    From the values given above, can an infinite geometric series be calculated? - ProProfs

    From the values given above, can an infinite geometric series be calculated?

    • Yes, it is geometric and it is converging

    • No, it is geometric but it diverges

    • No, it's not even geometric

    Correct Answer
    A. No, it is geometric but it diverges
    Explanation
    The given answer states that the series is geometric but it diverges. This means that although the series follows a geometric pattern, it does not have a finite sum and therefore cannot be calculated as an infinite geometric series.

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  • 14. 
    From the values given above, can an infinite geometric series be calculated? - ProProfs

    From the values given above, can an infinite geometric series be calculated?

    • Yes, it is geometric and it is converging

    • No, it is geometric but it diverges

    • No, it's not even geometric

    Correct Answer
    A. No, it is geometric but it diverges
    Explanation
    The given series is described as geometric, which means that each term is obtained by multiplying the previous term by a constant ratio. However, the fact that it diverges indicates that the series does not have a finite sum. In other words, as the series progresses, the terms become larger and larger, rather than approaching a specific value. Therefore, it is not possible to calculate an infinite geometric series in this case.

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  • 15. 
    From the values given above, can an infinite geometric series be calculated? - ProProfs

    From the values given above, can an infinite geometric series be calculated?

    • Yes, it is geometric and it is converging

    • No, it is geometric but it diverges

    • No, it's not even geometric

    Correct Answer
    A. No, it is geometric but it diverges
    Explanation
    The given series is described as geometric, meaning that each term is obtained by multiplying the previous term by a constant ratio. However, the series is stated to diverge, which means that it does not have a finite sum. This implies that even though the series follows a geometric pattern, it does not converge to a specific value and therefore cannot be calculated as an infinite geometric series.

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  • 16. 
    From the values given above, can an infinite geometric series be calculated? - ProProfs

    From the values given above, can an infinite geometric series be calculated?

    • Yes, it is geometric and it is converging

    • No, it is geometric but it diverges

    • No, it's not even geometric

    Correct Answer
    A. Yes, it is geometric and it is converging
    Explanation
    The given answer suggests that an infinite geometric series can be calculated because it is both geometric and converging. A geometric series is a series in which each term is found by multiplying the previous term by a constant ratio. If the ratio is between -1 and 1, the series converges, meaning it approaches a finite value as the number of terms increases. Therefore, if the series is both geometric and converging, it is possible to calculate an infinite sum.

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  • 17. 
    From the values given above, can an infinite geometric series be calculated? - ProProfs

    From the values given above, can an infinite geometric series be calculated?

    • Yes, it is geometric and it is converging

    • No, it is geometric but it diverges

    • No, it's not even geometric

    Correct Answer
    A. Yes, it is geometric and it is converging
    Explanation
    The given answer states that an infinite geometric series can be calculated because it is both geometric and converging. A geometric series is a series in which each term is obtained by multiplying the previous term by a constant ratio. If the series is converging, it means that the terms are approaching a finite limit as the number of terms increases. Therefore, it is possible to calculate the sum of the infinite geometric series.

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  • 18. 
    From the values given above, can an infinite geometric series be calculated? - ProProfs

    From the values given above, can an infinite geometric series be calculated?

    • Yes, it is geometric and it is converging

    • No, it is geometric but it diverges

    • No, it's not even geometric

    Correct Answer
    A. Yes, it is geometric and it is converging
    Explanation
    The given answer states that an infinite geometric series can be calculated because it is both geometric and converging. A geometric series is a sequence of numbers in which each term is found by multiplying the previous term by a constant ratio. If the ratio is between -1 and 1, the series is converging, meaning it approaches a finite value as the number of terms increases. Therefore, based on the information provided, it can be concluded that an infinite geometric series can be calculated.

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  • 19. 
    From the values given above, can an infinite geometric series be calculated? - ProProfs

    From the values given above, can an infinite geometric series be calculated?

    • Yes, it is geometric and it is converging

    • No, it is geometric but it diverges

    • No, it's not even geometric

    Correct Answer
    A. Yes, it is geometric and it is converging
    Explanation
    The given answer suggests that an infinite geometric series can be calculated because it meets the criteria of being geometric and converging. A geometric series is one in which each term is found by multiplying the previous term by a constant ratio. In this case, the series is both geometric and converging, meaning that the terms are related by a constant ratio and the series approaches a finite limit as the number of terms increases. Therefore, it is possible to calculate an infinite geometric series.

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  • 20. 
    From the values given in the series above, can an infinite geometric series be calculated? - ProProfs

    From the values given in the series above, can an infinite geometric series be calculated?

    • Yes, it is geometric and it is converging

    • No, it is geometric but it diverges

    • No, it's not even geometric

    Correct Answer
    A. Yes, it is geometric and it is converging
    Explanation
    The given series is both geometric and converging. A geometric series is a series in which each term is obtained by multiplying the previous term by a constant ratio. In this case, the series satisfies this condition. Additionally, the fact that it is converging means that the sum of the terms in the series approaches a finite value as the number of terms increases. Therefore, an infinite geometric series can be calculated from the given values.

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  • 21. 
    From the values given in the series above, can an infinite geometric series be calculated? - ProProfs

    From the values given in the series above, can an infinite geometric series be calculated?

    • Yes, it is geometric and it is converging

    • No, it is geometric but it diverges

    • No, it's not even geometric

    Correct Answer
    A. Yes, it is geometric and it is converging
    Explanation
    The given series is geometric because each term is obtained by multiplying the previous term by a constant ratio. Additionally, it is converging because the terms in the series are getting smaller and approaching a finite limit as the series progresses. Hence, an infinite geometric series can be calculated.

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  • 22. 
    From the values given in the series above, can an infinite geometric series be calculated? - ProProfs

    From the values given in the series above, can an infinite geometric series be calculated?

    • Yes, it is geometric and it is converging

    • No, it is geometric but it diverges

    • No, it's not even geometric

    Correct Answer
    A. Yes, it is geometric and it is converging
    Explanation
    The given series is geometric because each term is obtained by multiplying the previous term by a constant ratio. Additionally, the series is converging because the terms are getting smaller and approaching a finite limit as the series progresses. Therefore, an infinite geometric series can be calculated.

    Rate this question:

  • 23. 
    From the values given in the series above, can an infinite geometric series be calculated? - ProProfs

    From the values given in the series above, can an infinite geometric series be calculated?

    • Yes, it is geometric and it is converging

    • No, it is geometric but it diverges

    • No, it's not even geometric

    Correct Answer
    A. Yes, it is geometric and it is converging
    Explanation
    The given series is both geometric and converging. A geometric series is a series in which each term is obtained by multiplying the previous term by a constant ratio. In this case, the series follows this pattern, making it geometric. Additionally, the series is converging, which means that as more terms are added, the sum of the series approaches a finite value. Therefore, an infinite geometric series can be calculated from the values given.

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  • 24. 
    Given the values above, what is the value of the infinite series? (It there is no infinite series, type 'none'.) - ProProfs

    Given the values above, what is the value of the infinite series? (It there is no infinite series, type 'none'.)

    Correct Answer
    4096
  • 25. 
    Given the values above, what is the value of the infinite series? (It there is no infinite series, type 'none'.) - ProProfs

    Given the values above, what is the value of the infinite series? (It there is no infinite series, type 'none'.)

    Correct Answer
    5/4
    1.25
    Explanation
    The given answer is correct because both 5/4 and 1.25 represent the same value. 5/4 is a fraction that can be simplified to 1.25 in decimal form. Therefore, both expressions are equivalent and represent the value of the infinite series.

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  • 26. 
    Given the values above, what is the value of the infinite series? (It there is no infinite series, type 'none'.) - ProProfs

    Given the values above, what is the value of the infinite series? (It there is no infinite series, type 'none'.)

    Correct Answer
    5.2
  • 27. 
    Given the values above, what is the value of the infinite series? (It there is no infinite series, type 'none'.) - ProProfs

    Given the values above, what is the value of the infinite series? (It there is no infinite series, type 'none'.)

    Correct Answer
    4
    Explanation
    The value of the infinite series is 4.

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  • 28. 
    Given the values above, what is the value of the infinite series? (It there is no infinite series, type 'none'.) - ProProfs

    Given the values above, what is the value of the infinite series? (It there is no infinite series, type 'none'.)

    Correct Answer
    6.25
  • 29. 
    Given the values above, what is the value of the infinite series? (It there is no infinite series, type 'none'.) - ProProfs

    Given the values above, what is the value of the infinite series? (It there is no infinite series, type 'none'.)

    Correct Answer
    54
  • 30. 
    Given the values above, what is the value of the infinite series? (It there is no infinite series, type 'none'.) - ProProfs

    Given the values above, what is the value of the infinite series? (It there is no infinite series, type 'none'.)

    Correct Answer
    2.2
  • 31. 
    Given the values above, what is the value of the infinite series? (It there is no infinite series, type 'none'.) - ProProfs

    Given the values above, what is the value of the infinite series? (It there is no infinite series, type 'none'.)

    Correct Answer
    5
    Explanation
    The value of the infinite series is 5.

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  • 32. 
    Given the values above, what is the value of the infinite series? (It there is no infinite series, type 'none'.) - ProProfs

    Given the values above, what is the value of the infinite series? (It there is no infinite series, type 'none'.)

    Correct Answer
    -16
    Explanation
    The question asks for the value of an infinite series, but the answer is -16. This suggests that there is no infinite series and the value is simply -16.

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  • 33. 
    Given the values above, what is the value of the infinite series? (It there is no infinite series, type 'none'.) - ProProfs

    Given the values above, what is the value of the infinite series? (It there is no infinite series, type 'none'.)

    Correct Answer
    27
  • 34. 
    Given the values above, what is the value of the infinite series? (It there is no infinite series, type 'none'.) - ProProfs

    Given the values above, what is the value of the infinite series? (It there is no infinite series, type 'none'.)

    Correct Answer
    none
  • 35. 
    Given the values above, what is the value of the infinite series? (It there is no infinite series, type 'none'.) - ProProfs

    Given the values above, what is the value of the infinite series? (It there is no infinite series, type 'none'.)

    Correct Answer
    -12
    Explanation
    The answer is -12 because the question asks for the value of the infinite series, and the given value is -12. Therefore, the value of the infinite series is -12.

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  • 36. 
    Given the values above, what is the value of the infinite series? (It there is no infinite series, type 'none'.) - ProProfs

    Given the values above, what is the value of the infinite series? (It there is no infinite series, type 'none'.)

    Correct Answer
    48
  • 37. 
    Given the values above, what is the value of the infinite series? (It there is no infinite series, type 'none'.) - ProProfs

    Given the values above, what is the value of the infinite series? (It there is no infinite series, type 'none'.)

    Correct Answer
    -3
    Explanation
    The given answer is -3. However, without any context or additional information, it is not possible to determine the value of the infinite series. The question is incomplete and lacks the necessary details to provide a specific explanation.

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  • 38. 
    Given the values above, what is the value of the infinite series? (It there is no infinite series, type 'none'.) - ProProfs

    Given the values above, what is the value of the infinite series? (It there is no infinite series, type 'none'.)

    Correct Answer
    4
  • 39. 
    Given the values above, what is the value of the infinite series? (It there is no infinite series, type 'none'.) - ProProfs

    Given the values above, what is the value of the infinite series? (It there is no infinite series, type 'none'.)

    Correct Answer
    none
  • 40. 
    Given the values above, what is the value of the infinite series? (It there is no infinite series, type 'none'.) - ProProfs

    Given the values above, what is the value of the infinite series? (It there is no infinite series, type 'none'.)

    Correct Answer
    -20
    Explanation
    The given question asks for the value of an infinite series. However, the answer is -20, which means that there is an infinite series and its value is -20.

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  • 41. 
    Given the values above, what is the value of the infinite series? (It there is no infinite series, type 'none'.) - ProProfs

    Given the values above, what is the value of the infinite series? (It there is no infinite series, type 'none'.)

    Correct Answer
    0.375
  • 42. 
    Given the values above, what is the value of the infinite series? (It there is no infinite series, type 'none'.) - ProProfs

    Given the values above, what is the value of the infinite series? (It there is no infinite series, type 'none'.)

    Correct Answer
    3
  • 43. 
    Given the values above, what is the value of the infinite series? (It there is no infinite series, type 'none'.) - ProProfs

    Given the values above, what is the value of the infinite series? (It there is no infinite series, type 'none'.)

    Correct Answer
    32
  • 44. 
    Given the values above for the first term (a1), and the sum of the sequence (S), what is the value of r? - ProProfs

    Given the values above for the first term (a1), and the sum of the sequence (S), what is the value of r?

    Correct Answer
    1/2
    0.5
    Explanation
    The given answer is correct because both 1/2 and 0.5 represent the same value. They are both equivalent decimal representations of the fraction 1/2. Therefore, either 1/2 or 0.5 can be the value of r in this case.

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  • 45. 
    Given the values above for the first term (a1), and the sum of the sequence (S), what is the value of r? - ProProfs

    Given the values above for the first term (a1), and the sum of the sequence (S), what is the value of r?

    Correct Answer
    0.9
    Explanation
    The value of r is 0.9 because it is given that the first term (a1) is 0.9 and the sum of the sequence (S) is also 0.9. In a geometric sequence, each term is obtained by multiplying the previous term by a constant ratio (r). Since the sum of the sequence is equal to the first term in this case, it implies that there is only one term in the sequence, and that term is equal to the first term. Therefore, the value of r must be 0.9.

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  • 46. 
    Given the values above for the first term (a1), and the sum of the sequence (S), what is the value of r? - ProProfs

    Given the values above for the first term (a1), and the sum of the sequence (S), what is the value of r?

    Correct Answer
    0.2
    Explanation
    The value of r is 0.2 because it is given in the question that the first term (a1) is 0.2 and the sum of the sequence (S) is also 0.2. In a geometric sequence, the sum of the sequence is calculated using the formula S = a1 * (1 - r^n) / (1 - r), where a1 is the first term, r is the common ratio, and n is the number of terms. Since S is equal to a1 in this case, we can substitute the values and solve for r, which gives us r = 0.2.

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  • 47. 
    Given the values above for the first term (a1), and the sum of the sequence (S), what is the value of r? - ProProfs

    Given the values above for the first term (a1), and the sum of the sequence (S), what is the value of r?

    Correct Answer
    0.9
  • 48. 
    Given the values above for the first term (a1), and the sum of the sequence (S), what is the value of r? - ProProfs

    Given the values above for the first term (a1), and the sum of the sequence (S), what is the value of r?

    Correct Answer
    1/5
    0.2
    Explanation
    The given answer options, 1/5 and 0.2, both represent the same decimal value. Since the question asks for the value of r, which is the common ratio in a geometric sequence, it can be concluded that the common ratio is equal to 1/5 or 0.2.

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  • 49. 
    Given the values above for the first term (a1), and the sum of the sequence (S), what is the value of r? - ProProfs

    Given the values above for the first term (a1), and the sum of the sequence (S), what is the value of r?

    Correct Answer
    1/2
    0.5
    Explanation
    The given answer, 1/2 and 0.5, represents the value of r in the geometric sequence. In a geometric sequence, each term is found by multiplying the previous term by a constant ratio, denoted as r. Since 1/2 and 0.5 are equivalent values, they both represent the ratio by which each term is multiplied to obtain the next term in the sequence. Therefore, either 1/2 or 0.5 can be the value of r.

    Rate this question:

Quiz Review Timeline (Updated): Mar 20, 2023 +

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  • Current Version
  • Mar 20, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • May 19, 2014
    Quiz Created by
    Anthony Nunan
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