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?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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