Unit 3 Day 1 - Geometric Sequences.notebook · Unit 3 Day 1 Geometric Sequences.notebook September...
Transcript of Unit 3 Day 1 - Geometric Sequences.notebook · Unit 3 Day 1 Geometric Sequences.notebook September...
Unit 3 Day 1 Geometric Sequences.notebook September 26, 2018
Welcome!
Please get a new packet from the front chair and find your new seat.
Unit 3 Day 1 Geometric Sequences.notebook September 26, 2018
agenda 05 MIN Warm Up
25 MIN Unit 3: Lesson 1
15 MIN Assignment
Which one doesn't belong?
Unit 3 Day 1 Geometric Sequences.notebook September 26, 2018
Which one doesn't belong?
Unit 3:
Exponential FunctionsLearning Targets
• I can define a geometric sequence and find the common ratio
• I can write a recursive routine for a geometric sequence
Unit 3 Day 1 Geometric Sequences.notebook September 26, 2018
Geometric Sequence: a sequence where each term is just the previous term multiplied by a constant.
The constant is called the common ratio or the common multiplier
Recursion: where each step of a pattern is dependent on the step or steps before it.
These sequences are all RECURSIVE.
Recursive Formula Creates a sequence. It contains the following pieces:Starting value:
defines the nth term inrelation to the previous term (or terms)u0 or u1
The first number in the series.
Recursive rule or routine:
Condition:
tells which values of n the rule will work for.
Unit 3 Day 1 Geometric Sequences.notebook September 26, 2018
How to identify a geometric sequence...Are these geometric? If so, what is the common ratio?ex) 5, 10, 20, 40, ...
ex) 64.2, 40.446, 25.48098, 16.0530174
ex) 1, 1, 2, 3, 5, 8, ...
ex) 30, 10, 3.3, 1.1, ...
Arithmetic Sequence Geometric Sequence
Write a recursive routine to represent each type of sequence.
Unit 3 Day 1 Geometric Sequences.notebook September 26, 2018
Let's come up with a Recursive Formula to show the following pattern and find the next 3 terms. ex) 5, 20, 80, ___ , ___ , ____
ex) 30, 10, 3.3, 1.1, ...
Recursive Formula
Recursive Routine
Arithmetic or Geometric?
Is there a way to do this on my calculator?
Unit 3 Day 1 Geometric Sequences.notebook September 26, 2018
You MUST count how many iterations you have done.
5 enter
ans x 4 enter, enter, enter...
ex) 5, 20, 80, ___ , ___ , ___Recursive Formulau1 = 5
un = un1 x 4On your home screen type the following
Use this to find the 15th term! _________
Is there a FASTER way to do this on my calculator?
Actually, there are TWO other ways to do this on your calculator! I'll show you one way today and
the other on Friday.
Unit 3 Day 1 Geometric Sequences.notebook September 26, 2018
nMin() =
\u(n) = u(n1) * r (2nd 7 for u and XT0n for n)
u(nMin) = starting value
either 0 if u0 or 1 if u1/
1st change your mode: • Mode• Select Seq
Then go to y =
example:
OYO24, 12, 6, ...
Recursive Routine:
Arithmetic or Geometric?
Find the 15th term:
Unit 3 Day 1 Geometric Sequences.notebook September 26, 2018
OYO: Find the pattern for the number of black triangles!
Recursive Routine: Arithmetic or Geometric?
Find the number black triangles at stage 20.
Find the missing terms:
1) Arithmetic: 5,___ , ___, 14, ___, ___
2) Geometric: 48, ___, ___, 6, ___, ___
Unit 3 Day 1 Geometric Sequences.notebook September 26, 2018
ex) Every month, I take a count of the number of rabbits in my vegetable patch. The first month, I counted 12. The second month, 18, and the third month 27.
a) Starting value ______
b) Arithmetic or geometric? Common Difference or Ratio: _________
c) Recursive rule:
d) Find u8. What does this value mean?
Assignment:Geometric Sequences WS
Did you meet the goal? • I can define a geometric sequence and find the common ratio
• I can write a recursive routine for a geometric sequence
Unit 3 Day 1 Geometric Sequences.notebook September 26, 2018
Unit 3 Day 1 Geometric Sequences.notebook September 26, 2018