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Ram is working on Arithmetic progression, he find that the sum of first m term of an AP is xm2 + ym. Calculate the common difference of an AP.
1. 5x + y
2. 2x
3. 5y
4. 2x + y

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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 = xm+ ym

S1 = x + y = a= 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 = a- a11

⇒ d = 3x + y - (x + y)

⇒ d = 2x

∴ The common difference is 2x.

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