Chapter 3.6, Problem 7CYU

To determine

To determine the equation and the graph of the given sequence.

Answer to Problem 7CYU

  $a_n=55n+525$

Explanation of Solution

Given:

Sequence:

  $525,580,635,\mathrm{690...}$

Formula used:

nth term of any arithmetic progression is given by the formula:

  $t_n=a+(n-1)d$

  $t_n=$ nth term

  $a=$ The first term of the arithmetic progression

  $d=$ The common difference of the arithmetic progression

Calculation:

The common difference of the arithmetic progression is:

  $580-525=55$

Applying above formula,

  $\Rightarrow a_n=a+(n-1)d$

[In this case $n_0=525$ ]

  $\Rightarrow a_n=580+(n-1)(55)$  $[\because a=580,d=55]$

  $\begin{array}{l}\Rightarrow a_n=580+55n-55\\ \Rightarrow a_n=55n+525\end{array}$

So, the nth term of the sequence is $a_n=55n+525.$

Calculation for graph:

  $(n,a_n)$ represent the points of the graph.

First four points of the sequence is $(1,525),(2,580),(3,635),(4,690)$

Graph:

  

Interpretation:

From the graph it can be observed that the horizontal extent of the graph is from $-\infty$ to $\infty$ .

And the vertical extent of the graph is also from $-\infty$ to $\infty$ .

So, both the domain and range of the function is $(-\infty ,\infty )$ .