Chapter 12.1, Problem 17E

To determine

To calculate: The next four terms for the arithmetic sequence $5,-1,-7,\dots$ .

Answer to Problem 17E

The next four terms for the arithmetic sequence are $-13,-19,-25,-31$ .

Explanation of Solution

Given information:

The arithmetic sequence $5,-1,-7,\dots$ .

Formula used:

A sequence with first term as $a_1$ and next term written as sum of preceding term and common difference then it is called an arithmetic sequence. It is denoted as $a_1,a_1+d,a_1+2d+\dots$ .

Calculation:

Consider the arithmetic sequence $5,-1,-7,\dots$ .

Recall that a sequence with first term as $a_1$ and next term written as sum of preceding term and common difference then it is called an arithmetic sequence. It is denoted as $a_1,a_1+d,a_1+2d+\dots$ .

Compute the difference between the consecutive terms,

  $\begin{array}{c}{a}_2-a_1=-1-5\\ =-6\end{array}$

And

  $\begin{array}{c}{a}_3-a_2=-7+1\\ =-6\end{array}$

Therefore, common difference is $-6$ .

Now, fourth term is,

  $\begin{array}{c}{a}_4=a_3+\left(-6\right)\\ =-7-6\\ =-13\end{array}$

Now, fifth term is,

  $\begin{array}{c}{a}_5=a_4+\left(-6\right)\\ =-13-6\\ =-19\end{array}$

Next, sixth term is,

  $\begin{array}{c}{a}_6=a_5+\left(-6\right)\\ =-19-6\\ =-25\end{array}$

And, seventh term is,

  $\begin{array}{c}{a}_7=a_6+\left(-6\right)\\ =-25-6\\ =-31\end{array}$

Thus, the next four terms for the arithmetic sequence are $-13,-19,-25,-31$ .