1. 2.3 Finding the nth Term
Warm-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
3. Find the next 3 terms
E in the sequence
30°
A Z3, YY9, XXX27, ......
33° D
B
C
2. WU Answers:
L
11. T 15. M is the midpoint of AY
deductive
E 17. 48°, 17°, 62°
m<CPB
Q
13.
3. 2.3 Finding the nth Term pg. 106 to 111
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
5. What are we doing???
We are finding an equation (function rule) for a
pattern so we can find ANY term in the
sequence.
Think y = mx + b
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 + c
3. Substitute the constant difference for m
4. 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
6. Example:
Term 1 2 3 4 ... n
Value 5 7 9 11 ...
+2 +2 +2
f(n) = mn + c
f(n) = 2n + c
7 = 2 (2) + c
7 = 4 + c
-4 -4
3 = c SO---> f(n) = 2n + 3
This equation will give you ANY term in this sequence
7. Warm Up: Geometry
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 ....
8. Read over Example B and fill in chart.
What is the function rule?
Points dividing the line
Non-Overlapping Rays
Non-overlapping segments
Total
This function rule is also called a LINEAR FUNCTION!
Remember Slope intercept form--
ITS THE SAME THING!
