Question

Find the indicated term of each geometric sequence.

$7th$term of$0.1,1.0,10.0,.....$

Short answer

The$7th$term is${10}^5$.

Step-by-step solution

Step 1. Given information. 

We have, $0.1,1.0,10.0,.....$

$a_1=0.1,a_2=1.0,a_3=10.0$

The common ratio is

$$\begin{gathered} \frac{a_2}{a_1}=\frac{1.0}{0.1}=10 \\ \frac{a_3}{a_2}=\frac{10.0}{1.0}=10 \end{gathered}$$

The common ratio$r=10$.

To find the 7th term.

The $nth$ term of a geometric sequence is determined by formula $a_n=a_1{r}^{n-1}$

Substitute $a_1=0.1,r=10$and $n=7$

$$\begin{gathered} a_7=\left(0.1\right){\left(10\right)}^{7-1} \\ {a}_7=\left(0.1\right){\left(10\right)}^6 \\ {a}_7={10}^5 \end{gathered}$$