Question

Find the sum of the series:
$\left(i\right)2+5+8+..+182$

Answer 1

Given : $2+5+8+..+182$
First term, $a=2$
Last term, $l=182$
Common difference, $d=52=3$
Let the number of terms in given A. P. be n
$\therefore a_n=182$
The nth term of an A. P. is
$a_n=a+(n-1)d$
$\Rightarrow 182=2+3(n-1)$
$\Rightarrow 3(n-1)=180$
$\Rightarrow n=1+\frac{180}{3}$
$\Rightarrow n=61$
The sum of n terms of an A.P. is
$S_n=\frac{n}{2}[a+l]$
$\Rightarrow S_{61}=\frac{61}{2}[2+182]$
$\Rightarrow S_{61}=\frac{61}{2}\times 184$
$\Rightarrow S_{61}=5612$
Therefore, the sum of the given A.P. is $5612$