The 4th term of a G.P. is 16 and the 7th term is 128. Find the first term and common ratio of the series.
G.P.
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Question

The 4th term of a G.P. is 16 and the 7th term is 128. Find the first term and common ratio of the series.

KnowledgeBoat · Accepted Answer

Let first term be a and common ratio be r. We know that, nth term of a G.P. is given by, Tn = arn - 1 Given, 4th term of a G.P. is 16. ⇒ ar4 - 1 = 16 ⇒ ar3 = 16 ......(1) Given, 7th term is 128. ⇒ ar7 - 1 = 128 ⇒ ar6 = 128 ......(2) Dividing Equation (2) by Equation (1) : Substituting r = 2 in Equation 1, we get : ⇒ a(2)3 = 16 ⇒ a(8) = 16 ⇒ a = ⇒ a = 2. Hence, a = 2 and r = 2.

Mathematics

The 4th term of a G.P. is 16 and the 7th term is 128. Find the first term and common ratio of the series.

G.P.

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