Chapter 7.1, Problem 35E

Solution

To graph: The sequence $\frac{1}{2},\frac{3}{2},\frac{5}{2},\mathrm{.....},\frac{13}{2}$ .

Given information:

The given sequence is $\frac{1}{2},\frac{3}{2},\frac{5}{2},\mathrm{.....},\frac{13}{2}$ .

Graph:

Consider the given sequence:

  $\frac{1}{2},\frac{3}{2},\frac{5}{2},\mathrm{.....},\frac{13}{2}$

The first term is $\frac{2\left(1\right)-1}{2}=\frac{1}{2}$ , the second term is $\frac{2\left(2\right)-1}{2}=\frac{3}{2}$ , the third term is $\frac{2\left(3\right)-1}{2}=\frac{5}{2}$ , the fourth term is $\frac{2\left(4\right)-1}{2}=\frac{7}{2}$ , the fifth term is $\frac{2\left(5\right)-1}{2}=\frac{9}{2}$ , the sixth term is $\frac{2\left(6\right)-1}{2}=\frac{11}{2}$ , and the seventh term is $\frac{2\left(7\right)-1}{2}=\frac{13}{2}$ .

The rule of the sequence is: $a_n=\frac{2n-1}{2}$

These terms can be written as:

  $\left(1,\frac{1}{2}\right),\left(2,\frac{3}{2}\right),\left(3,\frac{5}{2}\right),\left(4,\frac{7}{2}\right),\left(5,\frac{9}{2}\right),\left(6,\frac{11}{2}\right),\left(7,\frac{13}{2}\right)$

Now to draw the graph by plotting these points on the graph:

  

Interpretation: The distance between the points $\left(1,\frac{1}{2}\right),\left(2,\frac{3}{2}\right),\left(3,\frac{5}{2}\right),\mathrm{..},\left(7,\frac{13}{2}\right)$ is increasing.