Chapter 8, Problem 32RE

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 32RE

First five terms of the arithmetic sequence are $8,6,4,2,0$ respectively.

Explanation of Solution

Given information:

An sequence is given with first term $a_1=8$ and common difference $d=-2$ .

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.

  $a_1=8$ and $d=-2$

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

  $\begin{array}{l}{a}_2=a_1+d=8-2=6\\ a_3=a_2+d=6-2=4\\ a_4=a_3+d=4-2=2\\ a_5=a_4+d=2-2=0\end{array}$

Hence, the first five terms of the sequence are $8,6,4,2,0$ respectively.

Now, the expression for nth term can be found as

  $\begin{array}{c}{a}_n=8+\left(n-1\right)\left(-2\right)\\ =8-2n+2\\ =10-2n\end{array}$

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.