Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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If the G.P.'S 5, 10, 20, ... and 1280, 640, 320, ... Have Their Nth Terms Equal, Find the Value of N. - Mathematics

If the G.P.'s 5, 10, 20, ... and 1280, 640, 320, ... have their nth terms equal, find the value of n.

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Solution

\[\text { Given }: \]

\[\text { First term, } a = 5 \]

\[\text { Common ratio }, r = 2\]

\[ a_n = \left( 5 \right) \left( 2 \right)^{n - 1} . . . \left( 1 \right)\]

\[\text { Similarly, } a_n = \left( 1280 \right) \left( \frac{1}{2} \right)^{n - 1} . . . \left( 2 \right)\]

\[\text { From }\left( 1 \right) \text { and } \left( 2 \right)\]

\[\left( 5 \right) \left( 2 \right)^{n - 1} = \left( 1280 \right) \left( \frac{1}{2} \right)^{n - 1} \]

\[ \Rightarrow \frac{1}{256} = \left( \frac{1}{4} \right)^{n - 1} \]

\[ \Rightarrow \left( \frac{1}{4} \right)^4 = \left( \frac{1}{4} \right)^{n - 1} \]

\[ \Rightarrow n - 1 = 4 \]

\[ \Rightarrow n = 5\]

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 20 Geometric Progression
Exercise 20.1 | Q 11 | Page 10
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