Chapter 11.3, Problem 4E

To determine

To calculate:

The slope of the graph of arithmetic sequence.

Answer to Problem 4E

The slope of the graph of arithmetic sequence is $\frac{5n-2}{n-1}$ .

Explanation of Solution

Given information:

Arithmetic sequence:

  $t_n=3+5\left(n-1\right)$

Formula used:

Slope:

  $m=\frac{y_2-y_1}{x_2-x_1}$

Where,

  $\left(x_1,y_1\right)$ = coordinates of first point in the line.

  $\left(x_2,y_2\right)$ = coordinates of second point in the line.

Calculation:

Consider the sequence $t_n=3+5\left(n-1\right)$

  $y_2-y_1=m\left(x_2-x_1\right)$

For arithmetic sequence slope,

  $\begin{array}{l}{a}_n-a_1=d\left(n-1\right)\\ 3+5\left(n-1\right)-a_1=d\left(n-1\right)\\ \frac{-2+5n}{n-1}\\ d=\frac{5n-2}{n-1}\end{array}$

Hence, the slope is $\frac{5n-2}{n-1}$ .