Question

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

$\left\{a_n\right\}=\left\{\frac{3^n}{n}\right\}$

Short answer

The first five terms of the given sequence are$3,\frac{9}{2},9,\frac{81}{4},\frac{243}{5}$

Step-by-step solution

Step 1. Write the given sequence.

The given sequence is$\left\{a_n\right\}=\left\{\frac{3^n}{n}\right\}$

Step 2. Find the five terms.

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

$$\begin{gathered} \left\{a_1\right\}=\left\{\frac{3^1}{1}\right\}=3 \\ \left\{a_2\right\}=\left\{\frac{3^2}{2}\right\}=\frac{9}{2} \\ \left\{a_3\right\}=\left\{\frac{3^3}{3}\right\}=9 \\ \left\{a_4\right\}=\left\{\frac{3^4}{3}\right\}=\frac{81}{4} \\ \left\{a_5\right\}=\left\{\frac{3^5}{5}\right\}=\frac{243}{5} \end{gathered}$$