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How Many Terms of the Series 2 + 6 + 18 + ... Must Be Taken to Make the Sum Equal to 728? - Mathematics

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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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 20 Geometric Progression
Exercise 20.3 | Q 6 | Page 28
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