Chapter 5.6, Problem 47E

To determine

To calculate: The next three terms for the arithmetic sequence $-5,-8,-11,-14,-17,\dots$ .

Answer to Problem 47E

The next three terms of the arithmetic sequence are $-20,-23,-26$ .

Explanation of Solution

Given information:

The arithmetic sequence $-5,-8,-11,-14,-17,\dots$ .

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 $-5,-8,-11,-14,-17,\dots$ .

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,

  $\begin{array}{c}{a}_2-a_1=-8+5\\ =-3\end{array}$

And

  $\begin{array}{c}{a}_3-a_2=-11+8\\ =-3\end{array}$

Therefore, common difference is $-3$ .

Now, sixth term is,

  $\begin{array}{c}{a}_6=a_5+\left(-3\right)\\ =-17-3\\ =-20\end{array}$

Now, seventh term is,

  $\begin{array}{c}{a}_7=a_6+\left(-3\right)\\ =-20-3\\ =-23\end{array}$

And, eight term is,

  $\begin{array}{c}{a}_8=a_7+\left(-3\right)\\ =-23-3\\ =-26\end{array}$

Thus, the next three terms of the arithmetic sequence are $-20,-23,-26$ .