Exercise 43 Page 205

Practice makes perfect

a We have been given three figures. Let's see if they follow a pattern.

Figure	Name	Number of Sides
1	Triangle	3
2	Square	4
3	Pentagon	5

For each figure the number of sides is one more than for the previous figure. By continuing this pattern we can determine the next three figures in the sequence.

Figure	Name	Number of Sides
1	Triangle	3
2	Square	4
3	Pentagon	5
4	Hexagon	6
5	Heptagon	7
6	Octagon	8

We are now going to draw these, one at the time. Let's begin with the hexagon, a polygon with six sides.

Our next polygon is seven-sided, which is called a heptagon.

Finally we will draw an octagon. This is a polygon with a total of eight sides.

b To describe the 20th figure we can write an equation for our sequence. Let's recall the equation for an arithmetic sequences, for which the first term is a_1 and the common difference is d.

a_n= a_1+(n-1) dWe know that with each new figure 1 side is being added. Therefore, our common difference is 1. Since the first figure is a triangle, we also know that the first term of the sequence is 3. a_n= a_1+(n-1) d ⇓ a_n= 3+(n-1) 1 By substituting 20 for n in the equation, we can find how many sides the 20th figure has.

a_n=3+(n-1)1

Substitute

n= 20

a_(20)=3+( 20-1)1

▼

Simplify right-hand side

MultByOne

a * 1=a

a_(20)=3+20-1

AddSubTerms

Add and subtract terms

a_(20)=22