Let a 1 , a 2 , a 3 … be in an A.P. such that ∑ k = 1 12 a 2 k − 1 = − 5 72 a 1 , a 1  = 0 . If ∑ k = 1 n a k = 0 , then n is:

Question

Let a 1 ​ , a 2 ​ , a 3 ​ … be in an A.P. such that ∑ k = 1 12 ​ a 2 k − 1 ​ = − 5 72 ​ a 1 ​ , a 1 ​  = 0 . If ∑ k = 1 n ​ a k ​ = 0 , then n is:

TestHub · Accepted Answer

Let a 1 ​ = a , common difference = d a 1 ​ + a 3 ​ + a 5 ​ + …… + a 23 ​ = − 5 72 ​ a 2 12 ​ [ 2 a + 11 × 2 d ] = − 5 72 ​ a 12 a + 132 d = − 5 72 ​ a 132 a + 132 × 5 d = 0 a = − 5 d 2 n ​ ( 2 a + ( n − 1 ) d ) = 0 ⇒ − 10 d + nd − d = 0 n = 11

Mathematics - Sequence & Series Question with Solution | TestHub

Options:

Doubts & Discussion

JEE Main (2028)