Question
In a geometric progression, the first term is 4 and the
common ratio is 2. If the sum of the first n terms is 252, what is the value of n?Solution
ATQ, For GP with first term a and ratio r ≠ 1: Sₙ = a (rⁿ − 1)/(r − 1) Here a = 4, r = 2, Sₙ = 252: 252 = 4(2ⁿ − 1)/(2 − 1) = 4(2ⁿ − 1) 2ⁿ − 1 = 252 / 4 = 63 2ⁿ = 64 ⇒ n = 6.
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