Question

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

$\left\{b_n\right\}=\left\{\frac{2n+1}{2n}\right\}$

Short answer

The first five terms of the given sequence are$\frac{3}{2},\frac{5}{4},\frac{7}{6},\frac{9}{8},\frac{11}{10}$

Step-by-step solution

Step 1. Write the given information.

The given sequence is$\left\{b_n\right\}=\left\{\frac{2n+1}{2n}\right\}$

Step 2. Find the next five terms.

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

role="math" localid="1646716932783" $$\begin{gathered} \left\{b_1\right\}=\frac{2·1+1}{2·1}=\frac{3}{2} \\ \left\{b_2\right\}=\frac{2·2+1}{2·2}=\frac{5}{4} \\ \left\{b_3\right\}=\frac{2·3+1}{2·3}=\frac{7}{6} \\ \left\{b_4\right\}=\frac{2·4+1}{2·4}=\frac{9}{8} \\ \left\{b_5\right\}=\frac{2·5+1}{2·5}=\frac{11}{10} \end{gathered}$$