Sn is the sum of the first n terms of a series given by Sn = n\(^2\) - 1. Find the nth term
A
4n + 1
B
4n - 1
C
2n + 1
D
2n - 1
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
\(S_{n} = n^{2} - 1\)
\(T_{n} = S_{n} - S_{n - 1}\)
\(S_{n - 1} = (n - 1)^{2} - 1\)
= \(n^{2} - 2n + 1 - 1\)
= \(n^{2} - 2n\)
\(S_{n} - S_{n - 1} = (n^{2} - 1) - (n^{2} - 2n)\)
= \(2n - 1\)
Source: Myschool Past Questions Archive (Record #30816)