Multiple choice

The geometric series $-4 + 16 - 64 + 256....$, $S_n = 52428$. Find the number of terms.

  1. $2$
  2. $4$
  3. $6$
  4. $8$
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D Correct answer
Explanation

This is a geometric series with a = -4 and r = -4. The sum formula is S_n = a(r^n - 1) / (r - 1). Substituting: 52428 = -4((-4)^n - 1) / (-5). 52428 * 5 / 4 = (-4)^n - 1. 65535 = (-4)^n - 1. 65536 = (-4)^n. Since (-4)^8 = 65536, n = 8.

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