Question

Sum of first 25 terms in AP is 525, sum of the next 25 terms is 725, what is the common difference?

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4. 

Explanatory Answer

The sum of the first 25 terms, S₂₅ = 525
The sum of the next 25 terms, K₂₅ = sum of next 25 terms = 725
a₂₆ = a₁ + 25d
a₂₇ = a₂ + 25d

K₂₅ = a₂₆ + a₂₇ + ...... + a₅₀
Or K₂₅ = a₁ + 25d + a₂ + 25d + ...... + a₂₅ + 25d
Or K₂₅ = a₁ + a₂ + ...... + a₂₅ + 25(25d)

Or K₂₅ = S₂₅ + 25(25d)
i.e., 725 = 525 + 25 x 25d
200 = 25 x 25d
8 = 25d
d =

Answer Choice (A)