Multiple choice

How many terms are to be added in the series $(8 + 6 +4 + \dots)$, to make the sum of $-52$ ?

  1. $3$
  2. $13$
  3. $12$
  4. $31$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The series is an arithmetic progression with first term a = 8 and common difference d = -2. Using the sum formula S = n/2 * (2a + (n-1)d), we set -52 = n/2 * (16 + (n-1)(-2)). Simplifying leads to -104 = 16n - 2n^2 + 2n, or n^2 - 9n - 52 = 0, which factors to (n-13)(n+4) = 0, giving n = 13.

AI explanation

This is an arithmetic progression with first term 8 and common difference -2. Using the sum formula S = n/2 times (2a + (n-1)d), we substitute the values to get -52 = n/2 times (16 + (n-1)(-2)). Solving the resulting quadratic equation, n squared minus 9n minus 52 equals 0, gives n = 13 as the positive root.

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