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CA Foundation · Quantitative Aptitude · Sequence and Series

How many terms of the GP 2, 6, 18, ... must be taken so that the sum is 728?

Six terms are needed. The sum of n terms of this GP simplifies to 3 to the power n minus 1. Setting that equal to 728 gives 3 to the power n equal to 729, which is 3 to the sixth, so n equals 6.

  1. A5
  2. B7
  3. C8
  4. D6Correct

Explanation

Sn = 2(3^n − 1)/(3 − 1) = 3^n − 1. Setting 3^n − 1 = 728 gives 3^n = 729 = 3^6, so n = 6. Check: 2 + 6 + 18 + 54 + 162 + 486 = 728. Choosing 7 results from mistakenly equating 3^n to 2187 or taking 3^n = 728 + 1 with a wrong power.

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