Question

If the sum of n terms of an A.P is given by $S_n = n^2 + n$, then the common difference of the A.P is

• A. 4
• B. 1
• C. 2
• D. 6

Answer 1

Answer: (C)

2

Answer 2

$S _{ n }= n ^{2}+ n$
$S _{1}=1+1=2= T _{1}$
$S _{2}=2^{2}+2=6= T _{1}+ T _{2}$
$\therefore T _{2}= S _{2}- S _{1}=4$
Common difference, $d = T _{2}- T _{1}$
$=4-2$
$=2$