Multiple choice

The sum of a certain number of terms of an AP series - 8, - 6, - 4, …… is 52. The number of terms is

  1. 12

  2. 13

  3. 11

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Sum = (n/2) * [2a + (n-1)d]. Here a = -8, d = 2, Sum = 52. 52 = (n/2) * [-16 + (n-1)2] = (n/2) * [2n - 18] = n(n - 9). n^2 - 9n - 52 = 0. Roots are n = 13 and n = -4. Since n must be positive, n = 13.

AI explanation

Using the arithmetic progression sum formula S = n/2 * (2a + (n-1)d), we substitute the first term a = -8, the common difference d = 2, and the sum S = 52. This gives the equation 52 = n/2 * (-16 + (n-1)2), which simplifies to 52 = n(n-9). The integer that satisfies this equation is 13.

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