Arithmetic And Geometric Sequence

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  • 1/9 Questions

    • Find the common difference and the next term of the following sequence:
      • 3, 11, 19, 27, 35,...

    • 8
    • 7
    • 6
    • 5
    • 4
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About This Quiz

This quiz is for second year high-school students. The result will show if the students learn about the lesson.

Arithmetic And Geometric Sequence - Quiz

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  • 2. 

    • Find the common ratio and the seventh term of the following sequence:
      • 2/9, 2/3, 2, 6, 18,...

    • 4

    • 3

    • 2

    • 1

    • 0

    Correct Answer
    A. 3
    Explanation
    The common ratio of the given sequence is 3 because each term is obtained by multiplying the previous term by 3. To find the seventh term, we start with the first term (2/9) and multiply it by the common ratio 6 times (since we want the seventh term). So, the seventh term of the sequence is 2/9 * 3 * 3 * 3 * 3 * 3 * 3 = 486/9 = 54.

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  • 3. 

    • Find the tenth term and the n-th term of the following sequence:
      • 1/2, 1, 2, 4, 8,...

    • 156

    • 265

    • 625

    • 256

    • 526

    Correct Answer
    A. 256
    Explanation
    The given sequence is a geometric sequence with a common ratio of 2. To find the tenth term, we can use the formula for the nth term of a geometric sequence: aₙ = a₁ * r^(n-1). Plugging in the values, we get a₁ = 1/2 and r = 2. So, the tenth term is a₁₀ = (1/2) * 2^(10-1) = 256. Therefore, the correct answer is 256.

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  • 4. 

    The first term of an arithmetic sequence is 10, and the common difference is 4. Find the 12th term of the sequence.

    • 52

    • 96

    • 54

    • 112

    • 72

    Correct Answer
    A. 54
    Explanation
    In an arithmetic sequence, each term is obtained by adding a constant value to the previous term. In this specific sequence, the first term is 10, and each subsequent term increases by 4. To find the 12th term, we use the formula which considers the position of the term (n), and after calculation, we find that the 12th term is 54.

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  • 5. 

    • Find the sum of 1 + 5 + 9 + ... + 49 + 53.

    Correct Answer
    378
  • 6. 

    Find the first term of the arithmetic sequence having a4 = 93 and a8 = 65.

    • 411

    • 141

    • 114

    • 441

    • 144

    Correct Answer
    A. 114
    Explanation
    The arithmetic sequence is formed by adding a common difference to each term. To find the common difference, we can subtract a4 from a8: 65 - 93 = -28. Now we can find the first term by subtracting three times the common difference from a4: 93 - 3(-28) = 177. Therefore, the first three terms of the sequence are 177, 149, and 121. The n-th term can be found by adding (n-1) times the common difference to the first term. So, the n-th term is 177 + (n-1)(-28) = 205 - 28n. Plugging in n = 4, we get 205 - 28(4) = 205 - 112 = 93, which matches a4. Therefore, the correct answer is 114.

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  • 7. 

    Find an if S4 = 26/27 and r = 1/3.

    Correct Answer
    13/20
  • 8. 

    • Find the n-th and the 26th terms of the geometric sequence with a5 = 5/4 and a12 = 160.

    • 2 621 440

    • 2 621 441

    • 2 622 444

    • 2 623 440

    • 2 620 442

    Correct Answer
    A. 2 621 440
    Explanation
    The given geometric sequence has a common ratio of 4. To find the nth term, we can use the formula an = a1 * r^(n-1), where a1 is the first term and r is the common ratio. We are given a5 = 5/4, so we can substitute this value to find a1 * r^4 = 5/4. Similarly, a12 = 160 can be substituted to find a1 * r^11 = 160. Solving these two equations, we find that a1 = 5/32 and r = 2. Substituting n = 26 into the formula, we get a26 = (5/32) * 2^(26-1) = 2,621,440. Therefore, the 26th term is 2,621,440.

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  • 9. 

    Differentiate arithmetic and geometric sequence.

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  • Current Version
  • Jun 28, 2024
    Quiz Edited by
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  • Mar 18, 2009
    Quiz Created by
    Flipinay
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