### CAT - questions and solution from progressions

Have given one interesting question from progressions. This is from challenge quiz I on our website. 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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Labels: CAT Progressions, CAT questions, CAT Solutions

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