Sequence And Series! Math Trivia Questions Quiz

The given arithmetic sequence has a common difference of 15. To find the first three terms, we can start with the first term, which is given as 10. Then, we add the common difference of 15 to find the second term, which is 10 + 15 = 25. Finally, we add the common difference again to find the third term, which is 25 + 15 = 40. Therefore, the first three terms of the sequence are 10, 25, and 40.

The difference between an arithmetic sequence and a geometric sequence lies in the way the terms are generated. In an arithmetic sequence, the terms are generated by adding a constant value, called the common difference, to the previous term. On the other hand, in a geometric sequence, the terms are generated by multiplying the previous term by a constant value, called the common ratio. Therefore, the correct answer is "Common difference and common ratio."

The sequence is decreasing by 4 each time. So, the next term would be 5 - 4 = 1. Following the same pattern, the term after that would be 1 - 4 = -3.

The given sequence does not follow a specific pattern such as arithmetic, constant, quadratic, or geometric. Instead, it combines different patterns within the sequence. The numbers 2, 2, 2, ... form a constant sequence, while the numbers 3, 6, 9, 12, ... form an arithmetic sequence with a common difference of 3. Therefore, the sequence can be classified as a combined sequence.

The given sequence 4;12;8;9;16;6;... does not follow a single pattern. It alternates between an arithmetic sequence (4, 8, 16) and a geometric sequence (12, 9, 6). In the arithmetic sequence, each term is obtained by adding a constant difference of 4. In the geometric sequence, each term is obtained by multiplying the previous term by a constant ratio of 0.75. Therefore, the correct answer is Geometric and Arithmetic Sequence.

The correct answer is 2.5 because it is the only number in the given list that is not an outlier. The other numbers, 1.5, 8, and -12, are all significantly different from the rest of the numbers and can be considered outliers. The number 2 is also an outlier, but since it is not the correct answer, it can be ignored. Therefore, the only valid number in the list is 2.5.

The given series is a geometric series with a common ratio of 1/2. To find the sum of the first 9 terms, we can use the formula for the sum of a geometric series: S = a(1 - r^n) / (1 - r), where a is the first term, r is the common ratio, and n is the number of terms. Plugging in the values, we get S = 32(1 - (1/2)^9) / (1 - 1/2) = 63.875. Therefore, the correct answer is 63.875.

The given sequence of numbers is being evaluated, which means that each number is being considered individually and analyzed. The numbers in the sequence are 156, 154, -154, -156, and 108. The answer, 156, is the first number in the sequence and is therefore the result of evaluating the given numbers.

The workers dig 1km each day and return to their base camp, so they travel a total of 2km each day. To find out how many days it will take them to travel 1260km, we divide 1260 by 2. This gives us 630 days. Therefore, the workers will have traveled a total of 1260km in the tunnel after 630/2 = 315 days. Since they return to their base camp each evening, we need to add 1 more day for the final trip back to the base camp, making the total 315 + 1 = 316 days. However, the question asks for the number of days, not including the final trip back to the base camp. Therefore, the correct answer is 316 - 1 = 315 days, which is equivalent to 35 days.

The given quadratic sequence starts with -2 and increases by 2, then 3, then 4, and so on. To find the term that will be equal to 322, we can observe that the difference between each term and its previous term is increasing by 1. So, the difference between the first and second term is 2, between the second and third term is 3, and so on. Using this pattern, we can calculate that the difference between the 24th and 25th term will be 25. Therefore, the 25th term of the sequence will be equal to 322.