Question
Let there be an $A.P.$ with first term $'a\ ',$ common difference $'d\ '.$ If $a_n$ denotes its $n^{\text {th }}$ term and $S_n$ the sum of first $n$ terms, find. $n$ and $S _{ n } ,$ if $a =5, d=3$ and $a _{ n }=50.$
✓
Answer
Given,
First term$(a) = 5$
Common difference $(d)=3$
and, term $\left(a_n\right)=50$
$\Rightarrow a+(n-1) d=50$
$\Rightarrow 5+(n-1)(3)=50$
$\Rightarrow 5+3 n-3=50$
$\Rightarrow 3 n=50-5+3$
$\Rightarrow 3 n=48$
$\Rightarrow n=\frac{48}{3}=16$
Therefore, $S _{ n }=\frac{n}{2}\left[a+a_n\right]$
$=\frac{16}{2}[5+50]$
$=8 \times 55$
$=440$
First term$(a) = 5$
Common difference $(d)=3$
and, term $\left(a_n\right)=50$
$\Rightarrow a+(n-1) d=50$
$\Rightarrow 5+(n-1)(3)=50$
$\Rightarrow 5+3 n-3=50$
$\Rightarrow 3 n=50-5+3$
$\Rightarrow 3 n=48$
$\Rightarrow n=\frac{48}{3}=16$
Therefore, $S _{ n }=\frac{n}{2}\left[a+a_n\right]$
$=\frac{16}{2}[5+50]$
$=8 \times 55$
$=440$
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