Chapter 9, Problem 76RE

To determine

To write : The first five terms of the series beginning with the given term, then calculate the first and second difference and state the type of model the sequence has..

Explanation of Solution

Given: The sequence is $a_1=-3$ and $a_n=a_{n-1}-2n$

The expression for $n^{\text{th}}$ term is given by,

  $a_n=a_{n-1}-2n$

So,

  $\begin{array}{c}{a}_1=-3\\ a_2=-3-4=-7\\ a_3=-7-6=-13\\ a_4=-13-8=-21\\ a_5=-21-10=-31\end{array}$

The first and second difference is calculated below.

  

The second differences are same. So, the given sequence is a perfect quadratic model.