Chapter 1.4, Problem 37HP

(a)

To determine

To calculate: To write the set of ordered pairs

Answer to Problem 37HP

There are four ordered pairs

Explanation of Solution

Given information:Arithmetic sequence is given

Calculation:

Arithmetic sequence given is as follows

Team Number	1	2	3	4
Term	4	7	10	13

Ordered pairs are

(1,4)

(2,7)

(3,10)

(4,13)

(b)

To determine

To calculate: To graph the ordered pairs for the function

Answer to Problem 37HP

Graph is sketched

Explanation of Solution

Given information:Arithmetic sequence is given

Calculation:

Arithmetic sequence given is as follows

Team Number	1	2	3	4
Term	4	7	10	13

On plotting the above points on graph,

  

(c)

To determine

To calculate: To describe the shape of graph

Answer to Problem 37HP

Graph is a straight line

Explanation of Solution

Given information:Arithmetic sequence is given

Calculation:

Graph of ordered pairs is as follows

  

Above graph is a straight line

(d)

To determine

To calculate: To write the rule to find the twentieth term.

Answer to Problem 37HP

The rule to find the twentieth term is $T_n=3n+1$

Explanation of Solution

Given information:Arithmetic sequence is given

Calculation:

Nth term of arithmetic sequence is calculated as

  $T_n=a+\left(n-1\right)d$

Where, $a=$ first number

  $n=$ term

  $d=$ common difference

Here,

  $a=4$

  $d=7-4=3$

Substituting the values, we get

  $\begin{array}{l}{T}_n=4+\left(n-1\right)3\\ T_n=4+3n-3\\ T_n=3n+1\end{array}$

Thus, rule to find the twentieth term is $T_n=3n+1$