Chapter 12.3, Problem 21AYU

To determine

To find: The fifth term and $nth$ term of the geometric sequence.

Answer to Problem 21AYU

The fifth term of the geometric sequence is $0$ and the $nth$ term is $\left(6\right){\left(-2\right)}^{n-1}$ .

Explanation of Solution

Given information:

The first term $a_1=0$ and the common ratio $r=\frac{1}{2}$ .

Calculation:

The formula for nth term of geometric sequence is given by,

  $a_n=a_1{r}^{n-1}$

Calculate the fifth term.

  $\begin{array}{c}{a}_5=\left(0\right){\left(\frac{1}{2}\right)}^{5-1}\\ =\left(0\right){\left(\frac{1}{2}\right)}^4\\ =0\end{array}$

Calculate the $nth$ term.

  $\begin{array}{c}{a}_n=\left(0\right){\left(\frac{1}{2}\right)}^{n-1}\\ =0\end{array}$

Therefore, the fifth term of the geometric sequence $0$ and the $nth$ term is $0$ .