Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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The Sum of N Terms of the G.P. 3, 6, 12, ... is 381. Find the Value of N. - Mathematics

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

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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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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 20 Geometric Progression
Exercise 20.3 | Q 8 | Page 28
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