Question

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

$a_1=-4$and$r=-2$

Short answer

The first five terms of the geometric sequence are$-4,8,-16,32,-64$.

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 $\left(a_1\right)=-4$

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

Second term:

$$\begin{gathered} a_2=a_{1}r \\ =(-4)(-2) \\ =8 \end{gathered}$$

The second term of the sequence is$8$.

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

Third term:

$$\begin{gathered} a_3=a_{2}r \\ =\left(8\right)(-2) \\ =-16 \end{gathered}$$

The third term of the sequence is $-16$.

Fourth term:

$$\begin{gathered} a_4=a_{3}r \\ =(-16)(-2) \\ =32 \end{gathered}$$

The fourth term of the sequence is $32$

Fifth term:

$$\begin{gathered} a_5=a_{4}r \\ =\left(32\right)(-2) \\ =-64 \end{gathered}$$

The fifth term of the sequence is $-64$.

Step 3. Write the first five terms of the sequence

The first five terms of the sequence are:

$-4,8,-16,32,-64$