Chapter 8.CT, Problem 1CT

To determine

To find:

The value of $a_{21}$ of the sequence whose nth term is given as $a_n={\left(-1\right)}^n\left(2n+1\right)$

Answer to Problem 1CT

Solution:

The value of $a_{21}$ in the sequence whose nth term is $a_n={\left(-1\right)}^n\left(2n+1\right)$ is $-43$

Explanation of Solution

Given:

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

Concept:

To find a particular term of a sequence, substitute the value of n in the given nth term

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

To find $a_{21}$, substitute $n=21$ in $a_n={\left(-1\right)}^n\left(2n+1\right)$ we get

$a_{21}={\left(-1\right)}^{21}\left[2\left(21\right)+1\right]$

$a_{21}=(-1)\left(42+1\right)$

$a_{21}=(-1)\left(43\right)$

$a_{21}=-43$

Conclusion:

So the value of $a_{21}$ is $-43$