Chapter 9, Problem 1RE

Writing the Terms of a Sequence In Exercises 1-4, write the first five terms of the sequence with the given n th term.

$a_n=6^n-2$

To determine

To calculate: The first five terms of the sequence $a_n=6^n-2$.

Answer to Problem 1RE

Solution:

The first five terms of the sequence are: $\underset{\_}{a_1=4,a_2=34,a_3=214,a_4=1294\text{ and }{a}_5=7774}$

Explanation of Solution

Given:

The sequence is $a_n=6^n-2$.

Calculation:

Consider the sequence $a_n=6^n-2$.

Here, put the value of $n=1,2,3,4,5$, to get $a_1,a_2,a_3,a_4\text{ and }{a}_5$ as shown below:

Substitute $n=1$, to get;

$\begin{array}{c}{a}_1=6^1-2\\ =6-2\\ =4\end{array}$

Substitute $n=2$, to get;

$\begin{array}{c}{a}_2=6^2-2\\ =36-2\\ =34\end{array}$

Substitute $n=3$, to get;

$\begin{array}{c}{a}_3=6^3-2\\ =216-2\\ =214\end{array}$

Substitute $n=4$, to get;

$\begin{array}{c}{a}_4=6^4-2\\ =1296-2\\ =1294\end{array}$

Substitute $n=5$, to get;

$\begin{array}{c}{a}_5=6^5-2\\ =7776-2\\ =7774\end{array}$

Hence, the five terms of the sequence are $a_1=4,a_2=34,a_3=214,a_4=1294\text{ and }{a}_5=7774$.