Multiple choice

Sum the series $25 + 21 + 17 + $... to $16$ terms.

  1. $80$
  2. $-80$
  3. $79$
  4. $-79$
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B Correct answer
Explanation

The series is arithmetic with first term a=25 and common difference d=-4. The sum of n terms is given by S_n = (n/2)(2a + (n-1)d). Plugging in n=16, a=25, and d=-4 gives S_16 = 8(50 + 15(-4)) = 8(50 - 60) = 8(-10) = -80.

AI explanation

This is an arithmetic progression with the first term a = 25, common difference d = -4, and number of terms n = 16. Using the arithmetic sum formula S = n/2 * [2a + (n - 1)d], we get 16/2 * [50 + (15 * -4)], which is 8 * [50 - 60] = 8 * -10. The sum of the series is -80.

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