Q. 24.2( 48 Votes )

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

Answer :

Given: 8^{th} of the G.P. is 192 and common ratio is 2.

That is,

a_{8} = 192 and r = 2.

We know that in G.P a_{n} = ar^{n-1}

Here, n: number of terms

a: First term = 5/2

r: common ratio

∴ a_{8} = a(2)^{8-1} (∵ r = 2 and n = 8)

⇒ 192 = a(2)^{7}

⇒ a × 128 = 192

Now,

∴ a_{12} = 3072

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