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.

x=n	-8	-4	-1	0	1
y=s(n)	1.00	2.00	2.75	3.00	3.25

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.

n	s(n)	0.25n+3	Do the values match?
-8	1.00	0.25(-8)+3=1	Yes
-4	2.00	0.25(-4)+3=2	Yes
-1	2.75	0.25(-1)+3=2.75	Yes
0	3.00	0.25(0)+3=3	Yes
1	3.25	0.25(1)+3=3.25	Yes

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