Multiple choice

What is the sum of first 6 terms of the series 64, -32, 16 ...?

  1. 22

  2. 32

  3. 42

  4. 52

  5. 86
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C Correct answer
Explanation

This is a geometric progression with a = 64 and r = -1/2. The sum of the first n terms is S_n = a(1 - r^n) / (1 - r). For n = 6, S_6 = 64(1 - (-1/2)^6) / (1 - (-1/2)) = 64(1 - 1/64) / (3/2) = 64(63/64) * (2/3) = 63 * 2/3 = 42.

AI explanation

This is a geometric progression with the first term a = 64 and the common ratio r = -0.5. Using the sum formula for a geometric progression, S = a(1 - r^n) / (1 - r), we find the sum of the first 6 terms is 64(1 - (-0.5)^6) / (1 - (-0.5)). Calculating this gives 64(1 - 1/64) / 1.5, which simplifies to 63 / 1.5 = 42.

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