Question

What is the common difference of an AP whose n${}^{th}$ term is $xn+y$?

• A. $x+y$
• B. $y$
• C. $x$
• D. $-x$

Answer 1

The correct option is C $x$

Given that, the $n^{th}$ term of an A.P. is $xn+y$.

To find out: The common difference of the A.P.

We know that, the common difference of an A.P. is the difference between any two consecutive terms.

That is, $d=a_{n+1}-a_n$

We have $a_n=xn+y$

$\therefore a_{n+1}=x(n+1)+y=nx+x+y$

Hence, $d=(nx+x+y)-(nx+y)$

$\Rightarrow nx+x+y-nx-y$

$\therefore d=x$

Hence, the common difference of the given A.P. is $x$.