Question

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

$5,10,20,40,...$

Short answer

The common ratio is $r=2$and the nth term of the geometric sequence is$a_n=5{\left(2\right)}^{n-1}$

Step-by-step solution

Step 1. Write the given information.

The given geometric sequence is$5,10,20,40,...$

Step 2. Find the common ratio.

$$\begin{gathered} a_1=5,a_2=10,a_3=20 \\ \frac{a_2}{a_1}=\frac{10}{5} \\ =2 \\ \frac{a_3}{a_2}=\frac{20}{10} \\ =2 \\ r=2 \end{gathered}$$

Step 3. Find the nth term.

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

$a_n=5·2^{n-1}$