Find the 12th term of a G.P. whose 8th term is 192 and the common ratio is 2.

Question

Find the 12^th term of a G.P. whose 8^th term is 192 and the common ratio is 2.

Asked by Abhisek | 1 year ago | 54

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Accepted Answer

The common ratio of the G.P., r = 2

And, let a be the first term of the G.P.

Now,

a₈ = ar ^8–1 = ar⁷

ar⁷ = 192

a(2)⁷ = 192

a(2)⁷ = (2)⁶ (3)

\( a=\dfrac{(2)^6\times 3}{(2)^7}=\dfrac{3}{2}\)

\( a_{12} = ar ^{12–1} = \dfrac{3(2)}{2}^{11}\)

(3)(2)¹⁰= 3072

Answered by Pragya Singh | 1 year ago