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?
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 + 12thterm = 0 Let 11thterm = k, common ratio = r 12thterm 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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