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# Find the $5^{th}$ term of an A.P. of $n$ terms whose sum is $n^2âˆ’2n$.

**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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