Question

If Sn, the sum of the first n terms of an A.P. is given by Sn = 2n2 + n, then
find its nth term.

Answer 1

The nth term of A.P. is 4n-1.

Explanation:

Given : The sum of the first n terms of an A.P. is given by $S_n=2n^2+n$

At n=1 , $S_1=2(1)^2+1=3$

At n=2 , $S_2=2(2)^2+2=10$

Since $a_1=S_1$

$S_2=a_1+a_2$

So , $a_1=3$

$a_1+a_2=10$

⇒$3+a_2=10\Rightarrow\ a_2=7$

Also, $a_2=a_1+d\Rightarrow\ d=a_2-a_1$

$d=7-3=4$

nth term of A.P. is given by :-

$a_n=a+(n-1)d\\\\=3+(n-1)(4)\\\\= 3+4n-4\\\\=4n-1$

Hence, the nth term of A.P. is 4n-1.

# Learn more :

If Sn' the sum of first n terms of an A.P is given by Sn = 5n2 + 3n then find its nth term

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Answer 2

The nth term of A.P. is 4n-1.

Explanation:

Given : The sum of the first n terms of an A.P. is given by

At n=1 ,

At n=2 ,

Since

So ,

⇒

Also,

nth term of A.P. is given by :-

Hence, the nth term of A.P. is 4n-1.