Question

The sum of n terms of an AP is $5n^2-3n$. Find the AP and hence find its 10th term

Answer 1

Given, the sum of $n$ terms of an A.P.$=5n^2-3n$

Putting $n=1$

$\Rightarrow 5n^2-3n=5\left(1\right)-3\left(1\right)=2$

Putting $n=2,$

$\Rightarrow 5n²-3n=5\left(4\right)-3\left(2\right)=14$

Therefore, 2nd term is

$S_2-n=14-2=12$

Therefore, A.P. is 2, 12, 22 ... and so on.

10th term $=a+9d$
$=2+9\times 10$
$=2+90$
$=92$

Hence, ${10}^{th}$ term is $92$.