Chapter 8.2, Problem 43E

To determine

To find: the tenthof the arithmetic sequence for given first two terms.

. Verify the result graphically.

Answer to Problem 43E

The tenth term of the arithmetic sequence is $59$ .

Explanation of Solution

Given information:

An sequence is given with first term $a_1=5$ and secondterm $a_2=11$ .

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 and second term of the sequence.

  $a_1=5$ and $a_2=11$

Consider dbe the common difference.

The common difference can be found by subtracting first term from second term.

  $\begin{array}{c}d=a_2-a_1\\ =11-5\\ =6\end{array}$

Now, the 10^th term will be

  $\begin{array}{c}{a}_n=a_1+\left(n-1\right)d\\ a_{10}=5+\left(10-1\right)\left(6\right)\\ =5+9\times 6\\ =5+54\\ =59\end{array}$

So, the nth term of the arithmetic sequence can be found as

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

Thus, the expression for the nth term of the arithmetic sequence is $a_n=6n-1$ .

Use the table feature of graphing utility to find the 10th 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,

$n$	$a_n$
1	$5$
2	$11$
3	$17$
4	$23$
5	$29$
6	$35$
7	$41$
8	$47$
9	$53$
10	$59$

Hence, the result is verified.