Chapter 12.1, Problem 6CFU

To determine

To calculate: The next four terms for the arithmetic sequence $6,11,16,\dots$ .

Answer to Problem 6CFU

The next four terms for the arithmetic sequence are 21,26,31,36 .

Explanation of Solution

Given information:

The arithmetic sequence $6,11,16,\dots$ .

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 $6,11,16,\dots$ .

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,

  $\begin{array}{c}{a}_2-a_1=11-6\\ =5\end{array}$

And

  $\begin{array}{c}{a}_3-a_2=16-11\\ =5\end{array}$

Therefore, common difference is 5.

Now, fourth term is,

  $\begin{array}{c}{a}_4=a_3+5\\ =16+5\\ =21\end{array}$

Now, fifth term is,

  $\begin{array}{c}{a}_5=a_4+5\\ =21+5\\ =26\end{array}$

Next, sixth term is,

  $\begin{array}{c}{a}_6=a_5+5\\ =26+5\\ =31\end{array}$

And, seventh term is,

  $\begin{array}{c}{a}_7=a_6+5\\ =31+5\\ =36\end{array}$

Thus, the next four terms for the arithmetic sequence are $21,26,31,36$ .