The sum of n terms of the G.P. 3, 6, 12, ... is 381.

Question:

The sum of n terms of the G.P. 3, 6, 12, ... is 381. Find the value of n.

Solution:

Here, a = 3

Common ratio, r = 3

Sum of n terms, Sn = 381

∴ Sn = 3 + 6 + 12 + ... + n terms

$\Rightarrow 381=3\left(\frac{2^{n}-1}{2-1}\right)$

$\Rightarrow 381=3\left(2^{n}-1\right)$

$\Rightarrow 127=2^{n}-1$

$\Rightarrow 2^{n}=128$

$\Rightarrow 2^{n}=2^{7}$

$\therefore n=7$

 

 

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