Chapter 12.1, Problem 33AYU

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

$1,-2,\text{ 3, }-4,\text{ 5, }-6,\mathrm{...}$

To determine

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

Answer to Problem 33AYU

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

Explanation of Solution

Given:

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

Calculation:

The given series is $1,-2,3,-4,5,-6,\dots .$

The first term is 1.

The second term is $-2$.

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

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