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Arithmetic Progressions — Maths STD 10 — Question

Gujarat BoardEnglish MediumSTD 10MathsArithmetic Progressions2 Marks
Question
Let there be an A.P. with first term ' $a$ ', common difference ' $d$ '. If $a_n$ denotes in $n^{\text {th }}$ term and $S_n$ the sum of first $n$ terms, find.
$k \text {, if } S_n=3 n^2+5 n \text { and } a k=164$
✓

Answer

$ a_k=s_k-s_{k-1} $
$ \Rightarrow 164=\left(3 k^2+5 k\right)-\left(3(k-1)^2+5(k-1)\right) $
$ \Rightarrow 164=3 k^2+5 k-3 k^2+6 k-3-5 k+5$
$⇒ 164 = 6k + 2$
$⇒ 6k = 162$
$⇒ k = 27$

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