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Let there be an A.P. with first term 'a', common difference 'd'. If an denotes in nth term and Sn the sum of first n terms, find. k , if S n = 3 n 2 + 5 n and a k = 164 - Mathematics

Sum

Let there be an A.P. with first term 'a', common difference 'd'. If an denotes in nth term and Sn the sum of first n terms, find.

\[k, \text{ if }  S_n = 3 n^2 + 5n \text{ and }  a_k = 164\]

 

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Solution

\[a_k = S_k - S_{k - 1} \]
\[ \Rightarrow 164 = \left( 3 k^2 + 5k \right) - \left( 3 \left( k - 1 \right)^2 + 5\left( k - 1 \right) \right)\]
\[ \Rightarrow 164 = 3 k^2 + 5k - 3 k^2 + 6k - 3 - 5k + 5\]
\[ \Rightarrow 164 = 6k + 2\]
\[ \Rightarrow 6k = 162\]
\[ \Rightarrow k = 27\]
\[\]

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APPEARS IN

RD Sharma Class 10 Maths
Chapter 5 Arithmetic Progression
Exercise 5.6 | Q 56.7 | Page 53
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