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CA Foundation · Quantitative Aptitude · Sequence and Series

The sum of the first 4 terms of a GP is 15 and the sum of the first 8 terms is 255. If the common ratio is positive, what is the first term?

The first term is 1. Since the sum of eight terms equals the sum of four terms times (1 + r to the power 4), 255 = 15(1 + r^4), so r^4 = 16 and r = 2. Then 15a = 15, giving a = 1.

  1. A1Correct
  2. B3
  3. C5
  4. D15/16

Explanation

S8 = S4(1 + r^4), so 255 = 15(1 + r^4), giving r^4 = 16 and r = 2. Then S4 = a(2^4 − 1)/(2 − 1) = 15a = 15, so a = 1. Check: 1+2+4+8 = 15 and the first 8 terms sum to 255.

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