If the first term of an A . P . is 3 and the sum of its first 25 terms is equal to the sum of its next 15 terms, then the common difference of this A . P . is

Question

If the first term of an A . P . is 3 and the sum of its first 25 terms is equal to the sum of its next 15 terms, then the common difference of this A . P . is, 1 6, 1 5, 1 4, 1 7

MARKS App · Accepted Answer

Sum of first 25 terms=sum of next 15 terms S 25 = S N e x t 15 ⇒ S 25 + S N e x t 15 = S 40 ⇒ 2 × S 25 = S 40 ⇒ 2 × 25 2 2 × 3 + 24 d = 40 2 2 × 3 + 39 d ⇒ 5 2 × 3 + 24 d = 4 2 × 3 + 39 d ⇒ 30 + 120 d = 24 + 156 d ⇒ 36 d = 6 ⇒ d = 1 6

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