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.


agenda 05 MIN Warm Up

25 MIN Unit 3: Lesson 1

15 MIN Assignment

Which one doesn't belong?


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


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.


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.


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?


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.


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:


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, ___, ___


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 · unit 3 day 1 geometric sequences.notebook september...

Documents