Chapter 12.2, Problem 28E

To determine

To calculate:

The seventh term of the geometric sequence $40,0.4,\mathrm{0.004...}$

Answer to Problem 28E

The seventh term of the geometric sequence $40,0.4,\mathrm{0.004...}$ is $0.00000000004$

Explanation of Solution

Given information:

  $40,0.4,\mathrm{0.004...}$

Formula used:

The common ratio is given by the following expression:

  $r=\frac{a_n}{a_{n-1}}$

The $n^{th}$ term of the geometric sequence is given by the following expression:

  $a_n=a_1{r}^{n-1}$

Calculation:

The given geometric sequence is considered as:

  $\begin{array}{l}{a}_1=40\\ a_2=0.4\\ a_3=0.004\end{array}$

Now, the common ratio is calculated as:

  $\begin{array}{l}r=\frac{a_2}{a_1}=\frac{0.4}{40}=0.01\\ r=\frac{a_3}{a_2}=\frac{0.004}{0.4}=0.01\end{array}$

The seventh term of the geometric sequence is calculated as:

  $\begin{array}{l}{a}_7=a_1{r}^{7-1}\\ a_7=40{\left(0.01\right)}^6\\ a_7=0.00000000004\end{array}$