Chapter 8, Problem 7Q

To determine

Find the rule for the $n\text{th}$ term of the sequence using graph.

Answer to Problem 7Q

The $n\text{th}$ term of the sequence is $a_n=0.25+\left(n-1\right)0.25$ .

Explanation of Solution

Given:

The given graph is

  

Calculation:

From the graph, the sequence is $0.25,0.5,0.75,1,1.25,---$

In an arithmetic sequence, the difference of consecutive terms, called the common difference, is constant.

Find the common difference between terms in the sequence $0.25,0.5,0.75,1,1.25,---$ .

  $\begin{array}{l}0.5-0.25=0.25\\ 0.75-0.5=0.25\\ 1-0.75=0.25\\ 1.25-1=0.25\end{array}$

The common difference $\left(0.25\right)$ is constant.

The general rule for the $n\text{th}$ term of the arithmetic sequence is $a_n=a_1+\left(n-1\right)d$ , where $a_1$ is first term and $d$ is the common difference.

Substitute the value of $a_1=0.25$ and $d=0.25$ in the rule.

  $a_n=0.25+\left(n-1\right)0.25$

Hence the $n\text{th}$ term of the sequence is $a_n=0.25+\left(n-1\right)0.25$ .