2.3 Nth Term
- 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
- 4. 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!
- 9. Example B pg. 108
- 11. Now try pg. 109 # 1-7 Odd 1. 6n-3, 117 3. 8n-12, 148 5. 4n-3, 797 7. n-2, 33