Question

In Problems 29–36, the given pattern continues. Write down the nth term of a sequence $\left\{a_n\right\}$suggested by the pattern.

$2,-4,6,-8,10,...$

Short answer

The nth term of the given sequence is$a_n={\left(-1\right)}^{n+1}·2n$.

Step-by-step solution

Step 1. Write the given information.

The given sequence is:

$2,-4,6,-8,10,...$

Step 2. Determine the pattern of the sequence and write down the nth term.

$a_1=2,a_2=-4,a_3=6,a_4=-8,a_5=10$

The pattern of the sequence is:

$$\begin{gathered} a_1={\left(-1\right)}^{1+1}·2·1=2 \\ {a}_2={\left(-1\right)}^{2+1}·2·2=-4, \\ {a}_3={\left(-1\right)}^{3+1}·2·3=6 \\ {a}_4={\left(-1\right)}^{4+1}·2·4=-8 \\ {a}_n={\left(-1\right)}^{n+1}·2n \end{gathered}$$