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CA Foundation · Quantitative Aptitude · Sequence and Series

The infinite series 20 + 10 + 5 + 2.5 + ... is a geometric series. What is its sum to infinity?

The sum to infinity is 40. The first term is 20 and the common ratio is one half, which is less than 1 in magnitude, so the sum is a divided by (1 minus r), that is 20 divided by 0.5, giving 40.

  1. A40Correct
  2. B30
  3. C80
  4. D35

Explanation

First term a = 20 and common ratio r = 10/20 = 1/2, so |r| < 1 and the sum exists. S = a/(1 - r) = 20/(1/2) = 40. The value 30 comes from wrongly using the denominator 1 + r = 1.5 (20/1.5 is not 30 either, but 30 would be obtained by adding only the first two terms), so it is wrong.

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