Question

sn=3n2+5n find nth term

Answer 1

GIVEN :

$S_n=3n^2+5n$ find nth term.

TO FIND :

The nth term of the given sequence.

SOLUTION :

Given that $S_n=3n^2+5n$

The formula for nth term of the sequence is given by :

$a_n=S_n-S_{n-1}$

From the given $S_n=3n^2+5n$  put n=n-1 , we get that,

$S_{n-1}=3(n-1)^2+5(n-1)$

$=3(n^2-2(n)(1)+1^2)+5n+5(-1)$

By using the Algebraic identity :

$(a-b)^2=a^2-2ab+b^2$

$=3(n^2-2n+1)+5n-5$

By using the Distributive property :

a(x-y)=ax-ay

$=3n^2+3(-2n)+3(1)+5n-5$

$S_{n-1}=3n^2-6n+3+5n-5$

$S_{n-1}=3n^2-n-2$

Substitute the values in the formula,

$a_n=3n^2+5n-(3n^2-n-2)$

$=3n^2+5n-3n^2+n+2$

$=6n+2$

$a_n=6n+2$

∴ the nth term of the given sequence is $a_n=6n+2$