# If the sum of the first 25 terms of the arithmetic progression is 525 and that of the next 25 terms is 725. Find the common difference.

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If the sum of the first 25 terms of the arithmetic progression is 525 and that of the next 25 terms is 725. Find the common difference.
1. 1/25
2. 8/25
3. 6/25
4. 4/25
5.

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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.