Question

The sum of first n terms of an AP is given by $S_n=2n^2+3n$, Find the first - term and second - term of AP.

• A. first term$=5$, second term$=9$
• B. first term$=6$, second term$=8$
• C. first term$=7$, second term$=10$
• D. first term$=4$, second term$=7$

Answer 1

The correct option is A first term$=5$, second term$=9$

$S_n=2n^2+3n$

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

$a_1=5$

$S_2=a_1+a_2$

$S_2=a_1+(a_1+d)$

$S_2=2a_1+d=2(2{)}^2+3(2)$

$=8+6=14$

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

$\Rightarrow d=4$

First term$=a_1=5$

Second term $=a_1+d$

$=5+4=9$.