Chapter 3.6, Problem 9PPS

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 9PPS

  $f\left(x\right)=3x-3$

The function is non-proportional.

Explanation of Solution

Given:

Given arithmetic sequence

  $0,3,6,\mathrm{...}$

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.

  $0,3,6,\mathrm{...}$

Let’s find the common difference.

  $d=3-0=3=6-3$

Now, the first term is $0$ .

So, nth term will be

  $\begin{array}{c}f\left(n\right)=a+\left(n-1\right)d\\ =0+\left(n-1\right)3\\ =3n-3\end{array}$

Hence, the required function will be

  $f\left(x\right)=3x-3$

Again,

  $\frac{6}{3}\ne \frac{3}{0}$

So, the function is non-proportional.