If the sum of first 11 terms of an A.P. , a 1 , a 2 , a 3 … … is 0 a 1 ≠ 0 then the sum of the A.P a 1 , a 3 , a 5 , … . . a 23 is k a 1 where k is equal to

Question

If the sum of first 11 terms of an A.P. , a 1 , a 2 , a 3 … … is 0 a 1 ≠ 0 then the sum of the A.P a 1 , a 3 , a 5 , … . . a 23 is k a 1 where k is equal to, - 121 10, 121 10, 72 5, - 72 5

MARKS App · Accepted Answer

Let a 1 be the first term and d be the common difference of A . P . ∴ S 11 = 0 ⇒ 11 2 2 a 1 + 10 d = 0 ⇒ a 1 + 5 d = 0 Now a 1 + a 3 + a 5 + … . + a 23 = 12 2 2 a 1 + 12 - 1 2 d = 12 a 1 + 11 d = 12 a 1 - 11 a 1 5 = - 72 a 1 5

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