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CA Foundation · Quantitative Aptitude · Sequence and Series

How many terms of the AP 5, 9, 13, 17, ... must be added to get a sum of 275?

11 terms are needed. With first term 5 and difference 4, the sum of n terms is n(2n+3). Setting this equal to 275 gives 2n²+3n-275=0, whose positive root is 11, and 11×25 equals 275.

  1. A10
  2. B12
  3. C11Correct
  4. D13

Explanation

Here a=5, d=4. Sn = n/2 [10 + 4(n-1)] = n(2n+3) = 275, so 2n²+3n-275=0. Factorising gives (2n+25)(n-11)=0, so n=11. Check: S11 = 11×25 = 275.

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