CA Foundation · Quantitative Aptitude · Sequence and Series
What is the sum to infinity of the geometric series 18 + 12 + 8 + 16/3 + ... ?
The sum to infinity is 54. The first term is 18 and the common ratio is 2/3, which is less than 1 in magnitude, so the series converges. Applying S = a/(1 - r) gives 18 divided by 1/3, which equals 54.
- A36
- B54Correct
- C45
- D72
Explanation
First term a = 18 and common ratio r = 12/18 = 2/3, which lies between -1 and 1. Sum to infinity = a/(1 - r) = 18/(1/3) = 54. The value 36 comes from wrongly dividing by (1 + r) = 5/3 incorrectly or by using r = 1/2 (18/(1/2)).
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