Correct Answer - Option 2 : 2x

**Given****∶**

Sum of first m term = xm2 + ym.

**Formula** **Used**∶

A_{n}= S_{n} - S_{n-1}

**Calculation****∶**

Common difference, d = a_{n} - a_{n-1}

Given that S_{m} = xm^{2 }+ ym

S_{1} = x + y = a_{1 }= first term [put m = 1]

S_{2} = 4x + 2y [put m = 2]

So, 2^{nd} term. a_{2} = S_{2} - S_{1}

a_{2} = 4x + 2y - (x + y)

a_{2} = 3x +y

Now, d = a_{2 }- a_{11}

⇒ d = 3x + y - (x + y)

⇒ d = 2x

**∴ The common difference is 2x.**