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 $( i)$
 
$\frac{2a+( 9-1)d}{2}=9-2$

$a+4d=7=5^{th}\ term$
Tutorialspoint
Tutorialspoint

Simply Easy Learning


Advertisements