Question

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

$a_1=-5$and$r=-3$

Short answer

The first five terms of the geometric sequence are$-5,15,-45,135,-405$

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 $\left(a_1\right)=-5$

Common ratio $\left(r\right)=-3$

Second term:

$$\begin{gathered} a_2=a_{1}r \\ =(-5)(-3) \\ =15 \end{gathered}$$

The second term of the sequence is$15$.

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

Third term:

$$\begin{gathered} a_3=a_{2}r \\ =15(-3) \\ =-45 \end{gathered}$$

The third term of the sequence is $-45$.

Fourth term:

$$\begin{gathered} a_4=a_{3}r \\ =(-45)\times (-3) \\ =135 \end{gathered}$$

The fourth term of the sequence is $135$.

Fifth term:

$$\begin{gathered} a_5=a_{4}r \\ =135\times (-3) \\ =-405 \end{gathered}$$

The fifth term of the sequence is$-405$.

Step 3. Write the first five terms of the sequence.

The first five terms of the sequence are:

$-5,15,-45,135,-405$.