Question

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

$\left\{c_n\right\}=\left\{{\left(-1\right)}^{n+1}{n}^2\right\}$

Short answer

The first five terms of the given sequence are$1,-4,9,-16,25$

Step-by-step solution

Step 1. Write the given sequence.

The given sequence is$\left\{c_n\right\}=\left\{{\left(-1\right)}^{n+1}{n}^2\right\}$

Step 2. Find the first five terms of the sequence.

To find the five terms in the given sequence we substitute

$1,2,3,4and5inton$

$$\begin{gathered} \left\{c_1\right\}=\left\{{\left(-1\right)}^{1+1}{1}^2\right\}=1 \\ \left\{c_2\right\}=\left\{{\left(-1\right)}^{2+1}{2}^2\right\}=-4 \\ \left\{c_3\right\}=\left\{{\left(-1\right)}^{3+1}{3}^1\right\}=9 \\ \left\{c_4\right\}=\left\{{\left(-1\right)}^{4+1}{4}^2\right\}=-16 \\ \left\{c_5\right\}=\left\{{\left(-1\right)}^{5+1}{5}^2\right\}=25 \end{gathered}$$