Question

the sum of n term of the AP is 2n2+5n then its first term is

Answer 1

Solution:

Given:

$\sf{\implies S_{n}=2n^{2}+5n}$

To Find:

=> nth term of A.P.

So we know that the nth term of an A.P. is given by,

$\sf{a_{n}=S_{n}-S_{n-1}}$

$\sf{a_{n}=(2n^{2}+5n)-[2(n-1)^{2}+5(n-1)]}$

By using the property,

(a - b)² = a² + b² - 2ab

So,

$\sf{a_{n} = (2n^{2}+5n)-[2(n^{2}+1-2n)+5(n-1)]}$

$\sf{\implies (2n^{2}+5n)-(2n^{2}+2-4n+5n-5)}$

$\sf{\implies 2n^{2}+5n-2n^{2}-2+4n-5n+5}$

$\sf{\implies 4n+3}$

${\boxed{\boxed{\bf{So,\;a_{n}=4n+3}}}}$