Chapter 9.2, Problem 40HP

To determine

To graph the ordered pairs( term number, term) and see whether the points lie on a line.

Answer to Problem 40HP

The equation of the line is $y=7x-4$ and the terms of AP lie on the line.

Explanation of Solution

Given information: Arithmetic sequence: 3, 10, 17, 24, 31, 38, .....

Concept Used: Let $a_1,a_2,a_3,\mathrm{....},a_n$ be the arithmetic sequence, the $n^{th}$ term of the A. P is

  $\begin{array}{l}{a}_n=(a+(n-1)d)\\ \text{where,}a-\text{first}\text{term}\text{;}d\text{-}\text{common}\text{difference}\end{array}$

Here, $a=3;d=7$ .

The $n^{th}$ term of the A. P is

  $a_n=(3+(n-1)7)=7n-4$

1. The ordered pairs are:

  $(1,3),(2,10),(3,17),(4,24),\mathrm{...}$

Using graphing utility and enter the ordered pairs as:

  $(1,3),(2,10),(3,17),\mathrm{...}$

The graph of the ordered pairs is given below as:

  

From the graph, it is concluded that the ordered pairs line on the line, whose function is given as: $y=7x-4$ and is analogous to the general term of the A.P.

1. From the location of the ordered pairs, it is seen that all the points lie in the first quadrant.

For $x=1.7,2.7or5.9$ , the value of $y$

1. does not lie on the given line. Since, at these values the sequence is not arithmetic and therefore, the points are not the part of the line.