Chapter 4, Problem 1CA

To determine

Which function represents the arithmetic sequence shown in the graph.

Answer to Problem 1CA

(C ) $f(n)=27-3n$ .

Explanation of Solution

Given information:The graph is given below.

  

From the graph,

The first term of arithmetic sequence is 24.

The second term of arithmetic sequence is 21.

The third term of arithmetic sequence is 18.

The fourth term of arithmetic sequence is 15.

So the arithmetic sequence is {24,21,18,15}.

Calculation:

Formula :

An explicit formula for the $n^{th}$ term of an arithmetic sequence is given below.

  $a_n=a_1+d(n-1)$ where $a_1$ is the first term and $d$ is the common difference.

So in the given arithmetic sequence $a_1$ =24.

The common difference can be found by subtracting the first term from the second term.

  $\begin{array}{c}d=a_{2_{}}-a_1.\\ d=21-24.\\ d=-3.\end{array}$

Substituting the common difference and first term of the arithmetic sequence into the formula.

  $\begin{array}{l}{a}_n=24+(-3)(n-1).\\ a_n=24-3n+3.\\ a_n=27-3n.\end{array}$

So the $n^{th}$ term of the arithmetic sequence if represented by function $f(n)=27-3n$ .

(C ) $f(n)=27-3n$ .