Question

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

$a_1=64$and$r=\frac{1}{4}$

Short answer

The first five terms of the geometric sequence are$64,16,4,1,\frac{1}{4}$.

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 $\left(a_1\right)=64$

Common ratio:

$\left(r\right)=\frac{1}{4}$

Second term:

$$\begin{gathered} a_2=a_{1}r \\ =64\times \frac{1}{4} \\ =16 \end{gathered}$$

The second term of the sequence is$16$.

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

Third term:

$$\begin{gathered} a_3=a_{2}r \\ =16\times \frac{1}{4} \\ =4 \end{gathered}$$

The third term of the sequence is $4$.

Fourth term:

$$\begin{gathered} a_4=a_{3}r \\ =4\times \frac{1}{4} \\ =1 \end{gathered}$$

The fourth term of the sequence is $1$.

Fifth term:

$$\begin{gathered} a_5=a_{4}r \\ =1\times \frac{1}{4} \\ =\frac{1}{4} \end{gathered}$$

The fifth term of the sequence is$\frac{1}{4}$.

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

The first five terms of the sequence are:

$64,16,4,1,\frac{1}{4}$.