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Question
How many terms of the series 2 + 6 + 18 + ... must be taken to make the sum equal to 728?
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Solution
Here,a = 2
Common ratio, r = 3
Sum of n terms, Sn = 728
\[S_n = 2\left( \frac{3^n - 1}{3 - 1} \right) \]
\[ \Rightarrow 728 = 2\left( \frac{3^n - 1}{2} \right)\]
\[ \Rightarrow 728 = 3^n - 1 \]
\[ \Rightarrow 3^n = 729\]
\[ \Rightarrow 3^n = 3^6 \]
\[ \therefore n = 6\]
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