Multiple choice

Directions: Answer the question independently. What is the sum of first 30 terms of the series 1, 3, 6, 10, 15, 21, 28….

  1. 5960

  2. 4960

  3. 4495

  4. 4060
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The series is 1, 3, 6, 10... which are triangular numbers. The n-th term is n(n+1)/2. Sum of first 30 terms = sum_{n=1 to 30} [n(n+1)/2] = 0.5 * [sum(n^2) + sum(n)]. Sum(n^2) = 30(31)(61)/6 = 9455. Sum(n) = 30(31)/2 = 465. Total sum = 0.5 * (9455 + 465) = 0.5 * 9920 = 4960.

AI explanation

This sequence is formed by triangular numbers, and the sum of the first n triangular numbers is given by the formula n(n + 1)(n + 2) / 6. To find the sum of the first 30 terms, substitute 30 into the formula to get 30 x 31 x 32 / 6. Multiplying these values gives 29760 / 6, which equals 4960.

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