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
Correct Answer: Option 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)