2.3 Finding the nth TermWarm-up: pg. 110 # 11-17 odd AND below

1. Write an example for inductive reasoning and deductive reasoning.

2. What is the measure of <ABC

A

B

C

D

E

33°

3. Find the next 3 terms in the sequence

Z3, YY9, XXX27, ......30°

WU Answers:

11.

13.

T

L

E

Q

15. M is the midpoint of AYdeductive

17. 48°, 17°, 62°m<CPB

READ and define function rule pg. 106

Complete Investigation pg. 106

What did you notice?

Remember your Algebra 1 !

Patterns and slope!!!!!!!!

Next Example A pg. 107

2.3 Finding the nth Term pg. 106 to 111

Example A pg. 107

What are we doing???We are finding an equation (function rule) for a pattern so we can find ANY term in the sequence.

How....1. Find the constant difference in the Values

(This is your m)2. Replace "x" with an "n" and "y" with "f(n)" and "c" for the "b"

f(n) = mn + c3. Substitute the constant difference for m4. Substitute any Term for "n" and its matching Value for "f(n)"5. Solve for "c"6. Go back to original BLANK equation and substitute the "m" and the "c". LEAVE "n" as "n"---now you have your function rule

Think y = mx + b

Example:

Term 1 2 3 4 ... nValue 5 7 9 11 ...

f(n) = mn + cf(n) = 2n + c 7 = 2 (2) + c 7 = 4 + c -4 -4

3 = c SO---> f(n) = 2n + 3

+2 +2 +2

This equation will give you ANY term in this sequence

Term 1 2 3 4 5 .... n

Value 4 7 10 13 16 .....

Term 1 2 3 4 ..... n

Value 12 6 0 -6 .....

Term 1 2 3 4 .... n

Value 6.5 7 7.5 8 ....

Warm Up: Geometry

Read over Example B and fill in chart.

What is the function rule?Points dividing the lineNon-Overlapping RaysNon-overlapping segmentsTotal

This function rule is also called a LINEAR FUNCTION!

Remember Slope intercept form--ITS THE SAME THING!

Example B pg. 108

1. 6n-3, 117 3. 8n-12, 148 5. 4n-3, 797 7. n-2, 33

Now try pg. 109 # 1-7 Odd