Sum of sequence

Algebra Level pending

The sequence { a k } \{a_k\} satisfies ∑ k = 1 n a k = n 2 + 1. \displaystyle \sum_{k=1}^{n}a_k=n^2+1. What is ∑ k = 1 2 n a 2 k ? \displaystyle \sum_{k=1}^{2n}a_{2k}?

2 n ( 4 n + 1 ) 2n(4n+1) 2 n ( 4 n + 2 ) 2n(4n+2) n ( 4 n + 1 ) n(4n+1) 2 n ( 2 n + 1 ) 2n(2n+1)

Sandeep Mehra by Sandeep Mehra , 23, India

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1 solution

Vishal Sharma
Jun 25, 2014

a(n)=2n-1 so the sum we need to find is an AP 3+7+11+......2n terms which can be found easily.

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