Chapter 3.6, Problem 43PFA

a.

To determine

To write: a function representing the given sequence.

Answer to Problem 43PFA

  $f(n)=9+3n$

Explanation of Solution

Given information: An arithmetic sequence 12,15,18,21 represents the number of sweatshirts sold at four consecutive games.

Since it is an arithmetic sequence whose first term $(a_1)$ =12, and common difference (d) = 15-12=3. Then its $n^{th}$ term is given by

  $\begin{array}{l}{a}_n=a_1+(n-1)d\\ a_n=12+(n-1)\times 3\\ a_n=12+3n-3=9+3n\end{array}$

So the corresponding function is given by,

  $f(n)=9+3n$

b.

To determine

To find: additional number of sweatshirts sold at each game.

Answer to Problem 43PFA

3

Explanation of Solution

Given information: An arithmetic sequence 12,15,18,21 represents the number of sweatshirts sold at four consecutive games

The additional number of sweatshirts sold at each game is given by common difference of above arithmetic sequence which is 3 sweatshirts.

c.

To determine

To graph: the above function and found its domain and range.

Answer to Problem 43PFA

Domain= $\left\{n/n\in N\right\}$

Range= $\left\{9+3n/n\in N\right\}$

Where $N$ is set of all natural number

Explanation of Solution

Graph:

d.

To determine

To find: the number of game in which number of sold sweatshirts is 45.

Answer to Problem 43PFA

12

Explanation of Solution

Here,

  $\begin{array}{l}f(n)=45\\ \Rightarrow 9+3n=45\\ \Rightarrow 3n=45-9=36\\ \Rightarrow n=\frac{36}{3}=12\end{array}$

Hence the required number of game is 12.