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 nth term.

$a_6=6^n-2$

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 provided 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 $a_n=6^n-2$ ;

Formula used:

Calculation:

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

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

Put $n=1$, to get;

$\begin{array}{ccc}\hfill a_1& =& 6^1-2\hfill \\ \hfill & =& 6-2\hfill \\ \hfill & =& 4\hfill \end{array}$

Put $n=2$, to get;

$\begin{array}{ccc}\hfill a_2& =& 6^2-2\hfill \\ \hfill & =& 36-2\hfill \\ \hfill & =& 34\hfill \end{array}$

Put $n=3$, to get;

$\begin{array}{ccc}\hfill a_3& =& 6^3-2\hfill \\ \hfill & =& 216-2\hfill \\ \hfill & =& 214\hfill \end{array}$

Put $n=4$, to get;

$\begin{array}{ccc}\hfill a_4& =& 6^4-2\hfill \\ \hfill & =& 1296-2\hfill \\ \hfill & =& 1294\hfill \end{array}$

Put $n=5$, to get;

$\begin{array}{ccc}\hfill a_5& =& 6^5-2\hfill \\ \hfill & =& 7776-2\hfill \\ \hfill & =& 7774\hfill \end{array}$

Thus, the five terms of the sequence are:

$a_1=4,a_2=34,a_3=214,a_4=1294\text{ and }{a}_5=7774$