nbsp-The sum of r nbsp-terms of an AP is 2r-2 - 3r- nbsp-The n-th- nbsp-term is -4n - 1-2n - 1-3n - 1-3n - 1-

The correct option is A 4n + 1 Given, S_r nbsp;= (2r^2 + 3r), the sum upto r terms of an AP. We know that the n^th term of AP is T_n nbsp;= S_n nbsp; S_ ...

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Standard X

Mathematics

Sum of n Terms of an AP

nbsp;The sum ...

Question

The sum of $r$ terms of an AP is $2 r^{2} + 3 r .$ The $n^{th}$ term is ___.

$2 n - 1$

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$4 n + 1$

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$3 n - 1$

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$3 n + 1$

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Solution

The correct option is B
$4 n + 1$

Given, $S_{r} = (2 r^{2} + 3 r),$ the sum upto $r$ terms of an AP.
We know that the $n^{th}$ term of AP is
$T_{n} = S_{n} - S_{n - 1} .$
$\Rightarrow S_{n} = 2 n^{2} + 3 n$ and
$S_{n - 1} = 2 {(n - 1)}^{2} + 3 (n - 1) .$

$∴ T_{n} = S_{n} - S_{n - 1}$
$= 2 n^{2} + 3 n - [2 (n^{2} - 2 n + 1) + 3 n - 3]$
$= 2 n^{2} + 3 n - 2 n^{2} + 4 n - 2 - 3 n + 3 = 4 n + 1$

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Q. The sum of 'r' terms of an AP is

2 r^{2} + 3 r

. The

n^{t h}

term of the AP is :

The sum of 'r' terms of an AP is $(2 r^{2} + 3 r)$ . Find its $n^{t h}$ term.

The sum of 'r' terms of an AP is $2 r^{2} + 3 r$ . Then, the $n^{t h}$ term is :

State if True or False. The sum of 'r' terms of an AP is $(2 r^{2} + 3 r)$ . The $n^{t h}$ term is 2n - 1

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The sum of r terms of an AP is 2r2+3r. The nth​ term is ___.

The correct option is B 4n+1 Given, Sr=(2r2+3r), the sum upto r terms of an AP. We know that the nth term of AP is Tn=Sn−Sn−1. ⇒Sn=2n2+3n and Sn−1=2(n−1)2+3(n−1). ∴Tn=Sn−Sn−1 =2n2+3n−[2(n2−2n+1)+3n−3] =2n2+3n−2n2+4n−2−3n+3 =4n+1

The sum of $r$ terms of an AP is $2 r^{2} + 3 r .$ The $n^{th}$ term is ___.