Chapter 8, Problem 31RE

To determine

To find: first five terms of the arithmetic sequence for given first term and common difference. Verify the result graphically.

Answer to Problem 31RE

First five terms of the arithmetic sequence are $3,7,11,15,19$ respectively.

Explanation of Solution

Given information:

An sequence is given with first term $a_1=3$ and common difference $d=4$ .

Concept used:

An arithmetic sequence of n terms, has the form $a_1,a_2,a_3,\mathrm{...},a_n$ and should have a common difference between each two consecutive terms.

That is

  $a_2-a_1=a_3-a_2=a_4-a_3=\mathrm{...}=a_n-a_{n-1}$

Common difference can be defined by d .

  $a_2-a_1=a_3-a_2=a_4-a_3=\mathrm{...}=a_n-a_{n-1}=d$

nth term of the arithmetic sequence has the form

  $a_n=a_1+\left(n-1\right)d$

Where $a_1$ is the first term of the sequence, and d is the common difference.

Calculation:

Now, consider the first term and the common difference.

  $a_1=3$ and $d=4$

First five terms of the sequence can be found as shown:

  $\begin{array}{l}{a}_2=a_1+d=3+4=7\\ a_3=a_2+d=7+4=11\\ a_4=a_3+d=11+4=15\\ a_5=a_4+d=15+4=19\end{array}$

Hence, the first five terms of the sequence are $3,7,11,15,19$ respectively.

Now, the expression for nth term can be found as

  $\begin{array}{c}{a}_n=3+\left(n-1\right)4\\ =3+4n-4\\ =4n-1\end{array}$

Use the table feature of graphing utility to find the first 5 terms of sequence by using following steps:

Press MODE key, select Seq in the fourth line and hit Enter

  

Press $Y=$ and Enter the sequence,

  

Set the table by pressing TBLSET and then press TABLE,

  

Hence, the result is verified.