Correct Answer - Option 2 : 8/25

**CALCULATION:**

In the Arithmetic Progression with common difference 'd' ,

Sum of the first 25 terms, S_{25} = 525

Sum of the next 25 terms, N_{25} = 725

If a_{1}, a_{2}, a_{3,}... are the terms of the arithmetic progression,

⇒ a26 = a1 + 25d

⇒ a_{27} = a_{2} + 25d and so on..

∴ N_{25} = a_{26} + a_{27} + a_{28} +....+ a_{50}

⇒ N_{25} = (a1 + 25d) + (a2 + 25d) + (a_{3} + 25d) +......+ (a_{25} + 25d)

⇒ N_{25} = (a_{1} + a_{2} + a_{3} +..... + a_{25}) + (25 × 25d)

⇒ N_{25} = S_{25 }+ 625d

⇒ 725 = 525 + 625d

⇒ 625d = 200

⇒ d = 200/625

⇒ **d = 8/25**

- The key to solving the above problem is to relate the sum of the first 25 terms with that of the next 25 terms.
- a
_{n} = a_{1} + (n - 1)d, where a_{n} = n^{th} term, a_{1} = first term, n = no.of terms in the AP, d = common difference.