Correct Answer - Option 2 : 2x
Given∶
Sum of first m term = xm2 + ym.
Formula Used∶
An= Sn - Sn-1
Calculation∶
Common difference, d = an - an-1
Given that Sm = xm2 + ym
S1 = x + y = a1 = first term [put m = 1]
S2 = 4x + 2y [put m = 2]
So, 2nd term. a2 = S2 - S1
a2 = 4x + 2y - (x + y)
a2 = 3x +y
Now, d = a2 - a11
⇒ d = 3x + y - (x + y)
⇒ d = 2x
∴ The common difference is 2x.