Question

If the sum of the n term of an AP is where p and q are constant the common the common difference is

Answer 1

Answer:

given ,

Sn=pn +qn^2

we know ,

Tn =Sn-S (n-1)

where Tn is nth term of AP

so,

Tn =pn+qn^2-q (n-1)^2-p (n-1)

=q (n^2-n^2+2n-1)+p (n-n+1)

=q (2n-1)+p

hence ,

Tn =q (2n-1)+p

put n=1 T1 = q+p

n=2 T2 =3q +p

common difference =T2-T1

=3q+p-q-p=2q

hence ,

common difference =2q