Question

In Problems 17–28, write down the first five terms of each sequence.

$\left\{a_n\right\}=\left\{\frac{n}{n+2}\right\}$

Short answer

The first five terms of the sequence are$\frac{1}{3},\frac{2}{4},\frac{3}{5},\frac{4}{6},\frac{5}{7}$

Step-by-step solution

Step 1. Write the given information.

The given sequence is$\left\{a_n\right\}=\left\{\frac{n}{n+2}\right\}$

Step 2. Find the five terms.

To find the five terms in the sequence we substitute $1,2,3,4and5inton$

$$\begin{gathered} \left\{a_1\right\}=\frac{1}{1+2}=\frac{1}{3} \\ \left\{a_2\right\}=\frac{2}{2+2}=\frac{2}{4} \\ \left\{a_3\right\}=\frac{3}{3+2}=\frac{3}{5} \\ \left\{a_4\right\}=\frac{4}{4+2}=\frac{4}{6} \\ \left\{a_5\right\}=\frac{5}{5+2}=\frac{5}{7} \end{gathered}$$