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CA Foundation · Quantitative Aptitude · Sequence and Series

The sum of an infinite GP is 20 and the sum of the squares of its terms is 100. What is the first term of the GP?

The first term is 8. From the two sums, dividing (sum)² by the sum of squares gives (1+r)/(1−r) = 4, so the ratio is 3/5. The first term then equals 20 × (1 − 3/5) = 8, and its squares sum to 64 ÷ (16/25) = 100.

  1. A5
  2. B10
  3. C8Correct
  4. D12

Explanation

a/(1−r) = 20 and a²/(1−r²) = 100. Dividing the square of the first by the second: a²/(1−r)² × (1−r²)/a² = 400/100 = 4, so (1+r)/(1−r) = 4, giving 1+r = 4−4r, r = 3/5. Then a = 20(1−3/5) = 8. Check: squares sum = 64/(1−9/25) = 64×25/16 = 100.

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