Question

In Problems 31–38, find the nth term $a_n$of each geometric sequence. When given, r is the common ratio.

$7,14,28,56,...$

Short answer

The common ratio is $r=2$and the nth term is$a_n=7·{\left(2\right)}^{n-1}$

Step-by-step solution

Step 1. Write the given information.

The given geometric sequence is$7,14,28,56,...$

Step 2. Find the common ratio.

$$\begin{gathered} a_1=7,a_2=14,a_3=28 \\ \frac{a_2}{a_1}=\frac{14}{7} \\ =2 \\ \frac{a_3}{a_2}=\frac{28}{14} \\ =2 \\ r=2 \end{gathered}$$

Step 3. Find the nth term.

The formula for nth terms is $a_n=a_1·r^{n-1}$

The nth term is$a_n=7·{\left(2\right)}^{n-1}$