If the sum of n terms of an A.P. is `(p n+q n^2)`, where p and q are constants, find the common difference.

Answer

N/a

Explanation

`"Here "S_(n)=pn+qn^(2)`
`rArr" "S_(n-1)=p(n-1)+q(n-1)^(2)`
`"Now "T_(n)=S_(n)-S_(n-1)`
`rArr" "T_(n)=pn+qn^(2)-p(n-1)-q(n-1)^(2)`
`=p+q(2n-1)`
`rArr" "T_(n-1)=p+q{2(n-1)-1}`
`=p+q(2n-3)`
`therefore" "d=T_(n)-T_(n-1)`
`=p+q(2n-1)-p-q(2n-3)`
Common difference d=2q