Chapter 8.1, Problem 45E

To determine

The correct graph for the given sequence.

  $a_n=\frac{2n-1}{n}$

Answer to Problem 45E

The correct match of graph is graph (b).

Explanation of Solution

Given Information:

The sequence is defined as,

  $a_n=\frac{2n-1}{n}$

Calculation:

Consider the given information,

  $a_n=\frac{2n-1}{n}$

Substitute 1 for n in the given sequence.

  $\begin{array}{c}{a}_1=\frac{2\left(1\right)-1}{1}\\ =1\end{array}$

Substitute 2 for n in the given sequence.

  $\begin{array}{c}{a}_2=\frac{2\left(2\right)-1}{2}\\ =1.5\end{array}$

Substitute 3 for n in the given sequence.

  $\begin{array}{c}{a}_3=\frac{2\left(3\right)-1}{3}\\ =1.6667\end{array}$

Substitute 4 for n in the given sequence.

  $\begin{array}{c}{a}_4=\frac{2\left(4\right)-1}{4}\\ =1.75\end{array}$

Substitute 5 for n in the given sequence.

  $\begin{array}{c}{a}_5=\frac{2\left(5\right)-1}{5}\\ =1.8\end{array}$

Make the table by using the given expression to intepret the limit.

$n$	$a_n=\frac{2n-1}{n}$
1	$1$
2	$1.5$
3	$1.667$
4	$1.75$
5	$1.8$

Now, make a scatter plot from the obtained points.

  

The obtained graph is matching with the graph (b).

Therefore, the correct option is option (b).