Exercise 28 Page 371

To help us see a pattern, let's use the first row of values as x-coordinates and the second row as y-coordinates and plot the corresponding points on a coordinate plane.

The five points on the plot seem to be on a straight line. If we assume this is a pattern, then the expression for s(n) is linear. s(n)=mn+b To find m and b, we can use any two points on the graph. Let's start with (0,3).

To find m let's choose an other point; for example, (1,3.25).

Using b=3 and m=0.25, we can now write a conjecture for s(n). s(n)=0.25n+3 Let's check this on the given values.

Since all values match, our conjecture gives a good expression for s(n). s(n)=0.25n+3