Chapter 12.2, Problem 10CFU

To determine

To calculate:

The $7^{th}$ term of the following geometric sequence:

  $7,2.1,0.63,\mathrm{...}$

Answer to Problem 10CFU

The $7^{th}$ term of geometric sequence is $0.005103$ .

Explanation of Solution

Given information:

  $7,2.1,0.63,\mathrm{...}$

Formula used:

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 series is considered as:

  $\begin{array}{l}{a}_1=7\\ a_2=2.1\\ a_3=0.63\\ a_7=?\end{array}$

The common ratio for the given geometric series is calculated as:

  $\begin{array}{l}r=\frac{a_2}{a_1}=\frac{2.1}{7}=0.3\\ r=\frac{a_3}{a_2}=\frac{0.63}{2.1}=0.3\end{array}$

Now, the $7^{th}$ term of the geometric sequence is calculated as:

  $\begin{array}{l}{a}_7=a_1{r}^{7-1}\\ a_7=\left(7\right){\left(0.3\right)}^{7-1}\\ a_7=0.005103\end{array}$