Correct Answer - Option 2 : 8/25
CALCULATION:
In the Arithmetic Progression with common difference 'd' ,
Sum of the first 25 terms, S25 = 525
Sum of the next 25 terms, N25 = 725
If a1, a2, a3,... are the terms of the arithmetic progression,
⇒ a26 = a1 + 25d
⇒ a27 = a2 + 25d and so on..
∴ N25 = a26 + a27 + a28 +....+ a50
⇒ N25 = (a1 + 25d) + (a2 + 25d) + (a3 + 25d) +......+ (a25 + 25d)
⇒ N25 = (a1 + a2 + a3 +..... + a25) + (25 × 25d)
⇒ N25 = S25 + 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.
- an = a1 + (n - 1)d, where an = nth term, a1 = first term, n = no.of terms in the AP, d = common difference.