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
jamb 1997mathematics

The correct answer is D. 2n - 1

\(S_{n} = n^{2} - 1\)

\(T_{n} = S_{n} - S_{n - 1}\)

\(S_{n - 1} = (n - 1)^{2} - 1\)

= \(n^{2} - 2n + 1 - 1\)

= \(n^{2} - 2n\)

\(S_{n} - S_{n - 1} = (n^{2} - 1) - (n^{2} - 2n)\)

= \(2n - 1\)

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