Chapter 3.6, Problem 10PPS

To determine

To find:an equation in function notation for the given arithmetic sequence. Check whether the function is proportional or non-proportional.

Answer to Problem 10PPS

  $f\left(x\right)=4x-8$

The function is non-proportional.

Explanation of Solution

Given:

Given arithmetic sequence

  $-4,0,4,\mathrm{...}$

Concept used:

Difference of consecutive term of an arithmetic sequence is constant.

nth term of an arithmetic sequence can be found by

  $f\left(n\right)=a+\left(n-1\right)d$

Where $a$ is 1^st term and common difference is $d$

Calculation:

Consider the given sequence.

  $-4,0,4,\mathrm{...}$

Let’s find the common difference.

  $d=0-\left(-4\right)=4=4-0$

Now, the first term is $-4$ .

So, nth term will be

  $\begin{array}{c}f\left(n\right)=a+\left(n-1\right)d\\ =-4+\left(n-1\right)4\\ =-4+4n-4\\ =4n-8\end{array}$

Hence, the required function will be

  $f\left(x\right)=4x-8$

Again,

  $\frac{0}{-4}\ne \frac{4}{0}$

So, the function is non-proportional.