Chapter 9.3, Problem 14E

To determine

To write: the first five terms of the geometric sequence.

Answer to Problem 14E

The first fife terms of sequence are $7,28,112,448,1792$ .

Explanation of Solution

Given information:

The given sequence,

  $a_1=7,r=4$

Concept used:

The $n$ th term of geometric sequence has the form $a_1=a_1{r}^{n-1}$ where $r$ is the common ratio of the consecutive terms of the sequence.

Every geometric sequence can be written in the following form.

  $a_1=a_1,a_2=a_{1}r,a_3=a_1{r}^2,a_4=a_1{r}^3,\mathrm{...},a_n=a_1{r}^{n-1},\mathrm{..}$

Calculation:

Consider the first term $a_1=7$ and common ratio $r=4$ :

Write first five terms as follows:

The first term is $a_1=7$ .

To find the second term, multiply first term 4 as shown below.

  $\begin{array}{c}{a}_2=a_{1}r\\ =7\cdot 4\\ =25\end{array}$

So, the second term is 28.

The 3^rd term can be calculated as

  $\begin{array}{c}{a}_3=a_{2}r\\ =28\cdot 4\\ =112\end{array}$

So, the third term is 112.

The 4^th term can be calculated as

  $\begin{array}{c}{a}_4=a_{3}r\\ =112\cdot 4\\ =448\end{array}$

So, the fourth term is 448.

The 5^th term can be calculated as

  $\begin{array}{c}{a}_5=a_{4}r\\ =448\cdot 4\\ =1792\end{array}$

So, the fifth term is 1792.

Therefore, the first five terms of sequence are $7,28,112,448,1792$ .