Question:
The sum of first n terms of an A.P is 5n2 + 3n. If its mth terms is 168, find the value of m. Also, find the 20th term of this A.P.
Solution:
$S_{n}=5 n^{2}+3 n$
We know
$a_{n}=S_{n}-S_{n-1}$
$\therefore a_{n}=5 n^{2}+3 n-5(n-1)^{2}-3(n-1)$
$a_{n}=10 n-2$
Now,
$a_{m}=168$
$\Rightarrow 10 m-2=168$
$\Rightarrow 10 m=170$
$\Rightarrow m=17$
$a_{20}=10(20)-2=198$