Question

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

$\left\{c_n\right\}=\left\{\frac{n^2}{2^n}\right\}$

Short answer

The first five terms of the given sequence are$\frac{1}{2},1,\frac{9}{8},1,\frac{25}{32}$

Step-by-step solution

Step 1. Write the given sequence.

The given sequence is$\left\{c_n\right\}=\left\{\frac{n^2}{2^n}\right\}$

Step 2. Find the five terms.

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

$$\begin{gathered} \left\{c_1\right\}=\frac{1^2}{2^1}=\frac{1}{2} \\ \left\{c_2\right\}=\frac{2^2}{2^2}=1 \\ \left\{c_3\right\}=\frac{3^2}{2^3}=\frac{9}{8} \\ \left\{c_4\right\}=\frac{4^2}{2^4}=1 \\ \left\{c_5\right\}=\frac{5^2}{2^5}=\frac{25}{32} \end{gathered}$$