Question

If the sum of $n$ terms of an $AP$ in $2n^2+5n$,then find the $4^{th}$ term.

Answer 1

$s_n=2n^2+5n$

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

$s_{n-1}=2n^2-4n+2+5n-5$

$T_n=s_n-s_{n-1}$

$T_n=2n^2+5n$$-2n^2+4n-2-5n+5$

$T_n=4n+3$

$T_4=4\times 4+3$

$T_4=19$

$4^{th}$of the given AP is $19$