Chapter 12.1, Problem 21E

To determine

To calculate: The next four terms for the arithmetic sequence $b,b+4,b+8,\dots$ .

Answer to Problem 21E

The next four terms for the arithmetic sequence are $b+12,b+16,b+20,b+24$ .

Explanation of Solution

Given information:

The arithmetic sequence $b,b+4,b+8,\dots$ .

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 $b,b+4,b+8,\dots$ .

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,

  $\begin{array}{c}{a}_2-a_1=b+4-b\\ =4\end{array}$

And

  $\begin{array}{c}{a}_3-a_2=b+8-b-4\\ =4\end{array}$

Therefore, common difference is $4$ .

Now, fourth term is,

  $\begin{array}{c}{a}_4=a_3+4\\ =b+8+4\\ =b+12\end{array}$

Now, fifth term is,

  $\begin{array}{c}{a}_5=a_4+4\\ =b+12+4\\ =b+16\end{array}$

Next, sixth term is,

  $\begin{array}{c}{a}_6=a_5+4\\ =b+16+4\\ =b+20\end{array}$

And, seventh term is,

  $\begin{array}{c}{a}_7=a_6+4\\ =b+20+4\\ =b+24\end{array}$

Thus, the next four terms for the arithmetic sequence are $b+12,b+16,b+20,b+24$ .