Sn is the sum of the first n terms of a series given by Sn = n\(^2\) – 1. Find the nth term
- 4n + 1
- 4n - 1
- 2n + 1
-
2n - 1
The correct answer is: D
Explanation
\(S_{n} = n^{2} - 1\)
\(T_{n} = S_{n} - S_{n - 1}\)
\(S_{n - 1} = (n - 1)^{2} - 1\)
= \(n^{2} - 2n + 1 - 1\)
= \(n^{2} - 2n\)
\(S_{n} - S_{n - 1} = (n^{2} - 1) - (n^{2} - 2n)\)
= \(2n - 1\)