Question

In the following exercises, write the first five terms of each geometric sequence with the given first term and common ratio.

$a_1=9$and$r=2$

Short answer

The first five terms of the geometric sequence are$9,18,36,72,144$.

Step-by-step solution

Step 1. Write the given information and find the second term with the help of the first term and common ratio.

The given information is:

First term$\left(a_1\right)=9$

Common ratio $\left(r\right)=2$

Second term:

$$\begin{gathered} a_2=a_{1}r \\ =9\times 2 \\ =18 \end{gathered}$$

The second term of the sequence is$18$.

Step 2. Find the next three terms in the same manner 

Third term:

$$\begin{gathered} a_3=a_{2}r \\ =18\times 2 \\ =36 \end{gathered}$$

The third term of the sequence is $36$.

Fourth term:

$$\begin{gathered} a_4=a_{3}r \\ =36\times 2 \\ =72 \end{gathered}$$

The fourth term of the sequence is$72$.

Fifth term:

$$\begin{gathered} a_5=a_{4}r \\ =72\times 2 \\ =144 \end{gathered}$$

The fifth term of the sequence is$144$.

Step 3. Write the first five terms of the sequence

The first five terms are$9,18,36,72,144$.