Question

The sum of the of first $n$ terms of an AP is given by $S_n=2n^2+3n$. Find the sixteen term of the A.P

Answer 1

$Sn=2n^2+3n$

$S_1=a_1=2(1{)}^2+3(1)=5$

$S_2=a_1+a_2$

$=a_1+(a_1+d)$

$=2a_1+d=2(2{)}^2+3(2)=8+6=14$

$2\times 5+d=14\Rightarrow d=4$

$a_1=5$

$T16=a_1+15d$

$5+15\times 4$

$=65$