Chapter 9.1, Problem 17E

To determine

To calculate: first five terms of the sequence.

Answer to Problem 17E

First five terms are $\left\{\frac{1}{3},\frac{1}{2},\frac{3}{5},\frac{2}{3},\frac{5}{7}\right\}$ .

Explanation of Solution

Given information: sequence $a_n=\frac{n}{n+2}$

Calculation:First five terms of sequence are $a_1,a_2,a_3,a_4,\text{and }{a}_5$

Putting $n=1$ for first term,

  $\begin{array}{l}{a}_1=\frac{1}{1+2}\\ a_1=\frac{1}{3}\end{array}$

Putting $n=2$ for second term,

  $\begin{array}{l}{a}_2=\frac{2}{2+2}\\ a_2=\frac{2}{4}\\ a_2=\frac{1}{2}\end{array}$

Putting $n=3$ for third term,

  $\begin{array}{l}{a}_3=\frac{3}{3+2}\\ a_3=\frac{3}{5}\end{array}$

Putting $n=4$ for fourth term,

  $\begin{array}{l}{a}_4=\frac{4}{4+2}\\ a_4=\frac{4}{6}\\ a_4=\frac{2}{3}\end{array}$

Putting $n=5$ for fifth term,

  $\begin{array}{l}{a}_5=\frac{5}{5+2}\\ a_5=\frac{5}{7}\end{array}$