Chapter 9.2, Problem 31E

To determine

To find the first five terms of the arithmetic sequence where $a_1=5$ and $d=6$ .

Answer to Problem 31E

  $a_1=5,a_2=11,a_3=17,a_4=23,a_5=29$

Explanation of Solution

Given information :

Let $a_1=5$ and $d=6$

Concept used:

The nth term of the arithmetic sequence has the form $a_n=a_1+\left(n-1\right)d$ , where $d$ is the common difference between the consecutive terms of the sequence and $a_1$ is the first term.

Calculations:

First, find out the formula for the nth term by substituting the value of the common difference $d=6$ and the first term $a_1=5$ in $a_n=a_1+\left(n-1\right)d$ .

So,

  $\begin{array}{c}{a}_n=a_1+\left(n-1\right)d\\ =5+\left(n-1\right)6\\ =5+6n-6\\ =6n-1\end{array}$

Now, first five terms of the sequence $a_n=6n-1$ will be:

  $\begin{array}{l}{a}_1=5\\ a_2=6\left(2\right)-1=11\\ a_3=6\left(3\right)-1=17\\ a_4=6\left(4\right)-1=23\\ a_5=6\left(5\right)-1=29\end{array}$

The terms of the arithmetic sequence are $a_1=5,a_2=11,a_3=17,a_4=23,a_5=29,\dots ,$ .