Multiple choice

If the sum of the sequence 1, 8, 15, 22….. is 154, find the number of terms in the sequence.

  1. 8

  2. 6

  3. 5

  4. 7
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D Correct answer
Explanation

This is an arithmetic progression with a = 1 and d = 6. The sum S_n = (n/2) * [2a + (n-1)d]. 154 = (n/2) * [2(1) + (n-1)6] = (n/2) * [2 + 6n - 6] = (n/2) * [6n - 4] = 3n^2 - 2n. 3n^2 - 2n - 154 = 0. Solving for n: (3n + 20)(n - 7) = 0. So n = 7.

AI explanation

This is an arithmetic progression with the first term a = 1 and the common difference d = 7. Using the sum formula S = n/2 [2a + (n - 1)d], we substitute the known values to get 154 = n/2 [2(1) + (n - 1)7]. Solving the equation 154 = n/2 (7n - 5) yields 7n^2 - 5n - 308 = 0, which factors to give the positive integer n = 7.

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