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Find the $5^{th}$ term of an A.P. of $n$ terms whose sum is $n^2−2n$.
Given: An A.P. of $n$ terms whose sum is $n^2-2n$.
To do: To find the $5^{th}$ term of the given A.P.
Solution:
$S_n=n^2-2n$
$\Rightarrow \frac{n}{2}( 2a+( n-1)d)=n( n-2)$
$\Rightarrow \frac{2a+( n-1)d}{2}=n-2\ \ .......( i)$
To get, $a_5=a+4d$, we put $n=9$ in $( i)$
$\frac{2a+( 9-1)d}{2}=9-2$
$a+4d=7=5^{th}\ term$
 
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