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Nth Term of a GP

The 7th term ...

Question

The 7^th term of a G.P. is 8 times the 4^th term. The G.P. when its 5^th term is 48, is.

4,8,16,32,....

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3,6,12,24,....

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5,25,125,.....

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Solution

The correct option is B 3,6,12,24,....
Given that t₇ = 8t₄ ⇒ ar⁶ = 8ar³
⇒ r³ = 8 = 23 ⇒ r = 2.

Also t₅ = 48 = ar⁴ = 48 or 16a = 48 ⇒ a = 3.

Hence the required G.P. is 3, 6, 12, 24 ……

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