Chapter 5.6, Problem 46E

To determine

To calculate: The next three terms for the arithmetic sequence $0,8,16,24,32,\dots$ .

Answer to Problem 46E

The next three terms of the arithmetic sequence are $40,48,56$ .

Explanation of Solution

Given information:

The arithmetic sequence $0,8,16,24,32,\dots$ .

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 $0,8,16,24,32,\dots$ .

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,

  $\begin{array}{c}{a}_2-a_1=8-0\\ =8\end{array}$

And

  $\begin{array}{c}{a}_3-a_2=16-8\\ =8\end{array}$

Therefore, common difference is $8$ .

Now, sixth term is,

  $\begin{array}{c}{a}_6=a_5+8\\ =32+8\\ =40\end{array}$

Now, seventh term is,

  $\begin{array}{c}{a}_7=a_6+8\\ =40+8\\ =48\end{array}$

And, eight term is,

  $\begin{array}{c}{a}_8=a_7+8\\ =48+8\\ =56\end{array}$

Thus, the next three terms of the arithmetic sequence are $40,48,56$ .