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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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