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.

$1,-2,3,-4,5,-6,...$

Short answer

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

Step-by-step solution

Step 1. Write the given information.

The given sequence is:

$1,-2,3,-4,5,-6,...$

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

$a_1=1,a_2=-2,a_3=3,a_4=-4,a_5=5,a_6=-6,...$

The pattern of the sequence is:

role="math" localid="1646671415796" $$\begin{gathered} a_1={\left(-1\right)}^{1+1}·1=1 \\ {a}_2={\left(-1\right)}^{2+1}·2=-2 \\ {a}_3={\left(-1\right)}^{3+1}·3=3 \\ {a}_4={\left(-1\right)}^{4+1}·4=-4 \\ {a}_n={\left(-1\right)}^{n+1}·n \end{gathered}$$