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      Question

      Sum of first 10 terms of a GP is equal to the sum of the

      first 12 terms in the same GP. Sum of the first 15 terms is 31, what is the third term in the GP?
      A -21 Correct Answer Incorrect Answer
      B 31 Correct Answer Incorrect Answer
      D -31 Correct Answer Incorrect Answer

      Solution

      Sum of first 10 terms is equal to sum of first 12 terms. Sum of first 12 terms = Sum of first 10 terms + 11th term + 12th term 11th term + 12th term = 0 Let 11th term = k, common ratio = r 12th term will be = kr k + kr = 0 k (1 + r) = 0 r = -1 as k cannot be zero Common ratio = -1 Now, sum of 15 terms = a(r - 1)/(r - 1) = 31 ⇒ a(-1 -1)/(-1 -1) = 31 ⇒ a = 31 ∴ Third term = ar = 31 × (-1) = 31

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