Have given one interesting question from progressions. This is from challenge quiz I. This is not that difficult, but as with all good questions, there is a formula-based method of solving them and there is a more straightforward intuitive way of solving them. (This question can be solved without putting pen to paper. Try it)

**Question**

Sum of first 25 terms in AP is 525, sum of the next 25 terms is 725, what is the common difference?
- 8/25
- 4/25
- 6/25
- 1/5

**Correct Answer**** :** 8/25. Correct Choice : (1)

**Explanatory Answer**

The sum of the first 25 terms, S_{25} = 525

The sum of the next 25 terms, K_{25} = sum of next 25 terms = 725

a_{26} = a_{1} + 25d

a_{27} = a_{2} + 25d

K_{25} = a_{26} + a_{27} + …… + a_{50}

Or K_{25} = a_{1} + 25d + a_{2} + 25d + …… + a_{25}+ 25d

Or K_{25} = a_{1} + a_{2} + …… + a_{25}+ 25(25d)

Or K_{25} = S_{25} + 25(25d)

i.e., 725 = 525 + 25 x 25d

200 = 25 x 25d

8 = 25d

d = 8/25

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