Chapter 9.1, Problem 38E

To determine

The expression for the apparent nth term

Answer to Problem 38E

  $a_n=n^2-1$

Explanation of Solution

Given:

The given sequence is

  $0,3,8,15,\mathrm{24.............}$

Calculation:

Consider that $a_i$ is the i^th term of the sequence

For $n=1,2,3,4,5,\mathrm{..................}n$

The terms are $0,3,8,15,\mathrm{24.............}{a}_n$

The terms can be written as

  $\begin{array}{l}=\left(1^2-1\right),\left(2^2-1\right),\left(3^2-1\right),\left(4^2-1\right),\left(5^2-1\right)\mathrm{.....................}{a}_n\\ =1-1,4-1,9-1,16-1,25-1,\mathrm{....................},a_n\\ =0,3,8,15,\mathrm{24................................}{a}_n\end{array}$

Therefore, the general term can be written as

  $a_n=n^2-1$