Question

If the sum of $n$ terms of $A.P.$ is $pn+q{n}^2$ where $p$ and $q$ are constants then common difference is?

• A. $p$
• B. $q$
• C. $2p$
• D. $2q$

Answer 1

Answer: (D)

$2q$

We are given the sum of $n$ terms of an A.P. to be $pn+q{n}^2$.

For $n=1$ in the given sum, we will get the first term and it is $p+q$.

For $n=2$ in the given sum, we get the sum of first and second term and it is $2p+4q$.

Now the second term = the sum of first two term - first term$=(2p+4q)-(p+q)=(p+3q)$.

The common difference of the A.P. is the difference between the first and second term and it is $(p+3q)-(p+q)=2q$.