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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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