Multiple choice

Find the sum of the first six terms of the following sequence. 64, -32, 16, ....

  1. 22

  2. 32

  3. 42

  4. 52

  5. 62
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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 sequence is a geometric progression with the first term a = 64 and a common ratio r = -0.5. We use the sum formula for a geometric progression, S = a(1 - r^n) / (1 - r), to find the sum of the first six terms by calculating 64(1 - (-0.5)^6) / (1 - (-0.5)). Working this out gives 64(1 - 1/64) / 1.5, which simplifies to 63 / 1.5. The result is 42.

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