Unit 10 Day 1 ­ Geometric Sequences
Welcome!
Please pick up a packet. Welcome! agenda
07 MIN Warm Up 25 MIN Lesson 10.1 Notes
15 MIN
Assignment Unit 10 Day 1 ­ Geometric Sequences
Plus
unıt 10:
exponentıal functıons
Learning Targets
I can define orally and in writing: sequence, term (u1), general term (un), recursive formula, recursive rule, arithmetic sequence, common difference, geometric sequence, common ratio I can write the recursive formula for an arithmetic and geometric sequence. I can read and write recursive formulas with subscript notation. I can find terms of a sequence given recursively. Unit 10 Day 1 ­ Geometric Sequences
warm up
[1] Two angles are supplementary and have a ratio of 1:4. What is the measure of the smaller angle?
a. 36 b. 18 c. 72 d. 45 e. 144
A
[2] One-half of the measure of the supplement of angle ABC is equal to twice the measure of angle ABC. What is the measure, in degrees, of the complement of angle ABC? a. 90 b. 18 c. 36 d. 72 e. 54
E
Recall from Semester 1...
Vocabulary:
Defn of Sequence: an ordered list of numbers
Each number in a sequence is called a _________.
Unit 10 Day 1 ­ Geometric Sequences
Arithmetic Sequence: is a sequence where each term is just the previous term plus a constant.
The constant is called the Common Difference
How to identify an arithmetic sequence...
Are these arithmetic? If so, what is the common difference?
ex) 2, 5, 8, 11, ...
ex) 10, 4, ­1, ­3, ...
ex) 91.4, 83.1, 74.8, 66.5, 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
How to identify a geometric sequence...
Are these geometric? If so, what is the common ratio?
ex) 5, 10, 20, 40, ...
30, 10, 3.3, 1.1, ...
ex) ex) 64.2, ­40.446, 25.48098, ­16.0530174
ex) 1, 1, 2, 3, 5, 8, ...
Unit 10 Day 1 ­ Geometric Sequences
These sequences are all RECURSIVE.
Recursion: where each step of a pattern is dependent on the step or steps before it.
Recursive Formula­ Creates a sequence. It contains the following pieces:
Starting value:
Recursive rule:
Condition:
The first number in the series.
defines the n th term in
relation to the previous term (or terms)
tells which values of n the rule will work for.
u0 or u1
Write a recursive routine to represent
each type of sequence.
Arithmetic Sequence
Geometric Sequence
Unit 10 Day 1 ­ Geometric Sequences
Let's come up with a recursive formula to
show the following pattern and find the next
3 terms.
ex) 5, 20, 80, ___ , ___ , ____
Arithmetic or Geometric?
Recursive Routine
ex) 30, 10, 3.3, 1.1, ...
Recursive Routine
Is there a way to do this on my
calculator?
Unit 10 Day 1 ­ Geometric Sequences
ex) 5, 20, 80, ___ , ___ , ___
Recursive Routine
u1 = 5
un = un­1 x 4
On your home screen type the following
5 enter
ans x 4 enter, enter, enter...
You MUST count how many iterations you
have done.
Use this to find the 15th term! _________
What if I don't want to count or
loose track while counting?
Unit 10 Day 1 ­ Geometric Sequences
ex) 5, 20, 80, ___ , ___ , ____
Recursive Routine
u1 = 5
un = un­1 x 4
Enter the starting term and value on your calculator like this:
{1, 5} then press enter.
Next, enter this:
{Ans (1)+1, Ans (2) x 4}
And keep hitting enter until you get to the term you need.
OYO
24, 12, 6, ...
Arithmetic or Geometric?
Recursive Routine:
Find the 15th term:
Unit 10 Day 1 ­ Geometric Sequences
OYO: Find the pattern for the number of
black triangles!
Arithmetic or Geometric?
Recursive Routine:
Find the number black triangles at stage 20.
Find the missing terms:
1) Arithmetic: 5,___ , ___, 14, ___, ___
2) Geometric: 48, ___, ___, 6, ___, ___ Unit 10 Day 1 ­ Geometric Sequences
ex) The amount of money Tony had in his lunch account before eating any lunches this year was $46. The amount remaining after the first day was $43.50. The amount remaining after the second day was $41. a) Starting value _________
b) Arithmetic or Geometric?
Common Difference or Ratio: _________
c) Recursive rule:
d) Find u10. What does this value mean?
e) When will Tony's account run out of money? ex) Every month, I take a count of the number of rabbits in her 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?
Unit 10 Day 1 ­ Geometric Sequences
Did you meet the goal?
I can define orally and in writing: sequence, term (u1), general term (un), recursive formula, recursive rule, arithmetic sequence, common difference, geometric sequence, common ratio I can write the recursive formula for an arithmetic and geometric sequence. I can read and write recursive formulas with subscript notation. I can find terms of a sequence given recursively. Assignment:
Geometric
Sequences WS
Unit 10 Day 1 ­ Geometric Sequences
Unit 10 Day 1 ­ Geometric Sequences