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  4. If the sum of n terms of an A.P is given by Sn = n2 + n, then the common difference of the A.P is

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Q. 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

KCETKCET 2020

Solution:

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