Chapter 12.1, Problem 14E

To determine

Calculate the first five term of the given sequence.

Answer to Problem 14E

The first five term of the sequence are $-8,-4,-2,-1,\frac{-1}{2}$ .

Explanation of Solution

Given:

It is given in the question that the sequence is $a_n=\frac{a_{n-1}}{2}and{a}_1=-8$ .

Concept Used:

In this, use the concept of arithmetic progression in which put the number and calculate the problem.

Calculation:

Here, the sequence is $a_n=\frac{a_{n-1}}{2}and{a}_1=-8$ .

First, find $a_2$ ,

  $\begin{array}{l}{a}_n=\frac{a_{n-1}}{2}\left\{nthterm\right\}\\ a_2=\frac{a_{2-1}}{2}\{n=2\}\\ a_2=\frac{a_1}{2}\{a_1=-8\}\\ a_2=\frac{-8}{2}\\ a_2=-4\end{array}$

Next, find $a_3$ ,

  $\begin{array}{l}{a}_n=\frac{a_{n-1}}{2}\left\{nthterm\right\}\\ a_3=\frac{a_{3-1}}{2}\{n=3\}\\ a_3=\frac{a_2}{2}\{a_2=-4\}\\ a_3=\frac{-4}{2}\\ a_3=-2\end{array}$

Next, find $a_4$ ,

  $\begin{array}{l}{a}_n=\frac{a_{n-1}}{2}\left\{nthterm\right\}\\ a_4=\frac{a_{4-1}}{2}\{n=4\}\\ a_4=\frac{a_3}{2}\{a_3=-2\}\\ a_4=\frac{-2}{2}\\ a_4=-1\end{array}$

Finally find $a_5$ ,

  $\begin{array}{l}{a}_n=\frac{a_{n-1}}{2}\left\{nthterm\right\}\\ a_5=\frac{a_{5-1}}{2}\{n=5\}\\ a_5=\frac{a_4}{2}\{a_4=-1\}\\ a_5=\frac{-1}{2}\end{array}$

Conclusion:

The first five term of the sequence are $-8,-4,-2,-1,\frac{-1}{2}$ .