Chapter 12.1, Problem 31AYU

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

$1,-1,1,-1,1,-1,\mathrm{...}$

To determine

To find: The nth term of a sequence $\left\{a_n\right\}$ suggested by the pattern.

Answer to Problem 31AYU

$\left\{a_n\right\}\text{ = }{\left(-1\right)}^{n+1}$

Explanation of Solution

Given:

$1,-1,1,-1,1,-1,\dots$

Calculation:

The given series is $1,-1,1,-1,1,-1,\dots$

The first term is 1.

The second term is $-1$.

The nth term will be ${\left(-1\right)}^{n+1}$.

$\left\{a_n\right\}\text{ = }{\left(-1\right)}^{n+1}$