The sum of the first 15 terms in an arithmetic progression is 200 , while the sum of the next 15 terms is 350 . Then the common difference is
Explanation:
Sum of n terms of an AP = n/2 × [2a + (n - 1)d]
Sum of first 15 terms = 200 ∴ 200 = 15/2 × (2a + 14d) ⇒ 2a + 14d = 80/3 ...(1)
Sum of first 30 terms = 200 + 350 = 550 ∴ 550 = 30/2 × (2a + 29d) ⇒ 2a + 29d = 110/3 ...(2)
(2) - (1), we get 15d = 30/3 ⇒ d = 10/15 = 2/3
Hence, option (b).
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