The sum of first n terms of an A.P is 5n2 + 3n.

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,

$a_{m}=168$

$\Rightarrow 10 m-2=168$

$\Rightarrow 10 m=170$

$\Rightarrow m=17$

$a_{20}=10(20)-2=198$

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