Day 1 Geometric Sequences.notebook
March 13, 2017
Date: Monday 3/13
Objective: I can write a rule for and find the nth term of a geometric sequence.
Entry: Find the next three terms in each pattern. A.
B.
C.
unit 6
EXPONENTIAL FUNCTIONS
NOTES
Geometric Sequences: A sequence where the ratio of successive terms is a constant, r. 'r' is called the common ratio. Geometric sequences are like functions ­ the position is the input, and the term is the output.
1
Day 1 Geometric Sequences.notebook
March 13, 2017
Notes
Example: 3, 6, 12, 24, ...
Geometric Sequence
Vocabulary:
Two ways to describe a pattern based on a common ratio (r)
Recursive: gives the next term based on the previous
f(n) = f(n­1) r
must give f(1)=__ [first term] n ≥ 2
Explicit: gives any(nth) term based on the term number
f(n) = f(0) r(n)
n≥1
Example 1:
Write an explicit and a recursive rule for...
1. Make a table. 3, 12, 48, 192, ...
n
0
1
2
3
f(n)
2. What is the pattern or common ratio? r=__
3. Rec. f(n) = f(n­1) __ ; f(1) = __
4. Exp. f(n) = __ __
(n)
2
Day 1 Geometric Sequences.notebook
March 13, 2017
Example 2:
Write an explicit and a recursive rule for...
1. Make a table. 9, 3, 1 ...
n
0
1
2
3
f(n)
2. What is the pattern or common ratio? r=__
3. Rec. f(n) = f(n­1)__ ; f(1) = __
4. Exp. f(n) = __ __
(n)
Example 3: Find the explicit formula and the term
named in the problem.
8, ­16, 32, ­64 ...
Find f(12)
1. Make a table.
n
0
1
2
3
f(n)
2. What is the pattern or common ratio? r=__
3. Exp. f(n) = __ __
4. Find f(12) =
(n)
3
Day 1 Geometric Sequences.notebook
March 13, 2017
Example 4:
Given a recursive formula for a geometric sequence find
the first five terms.
Class work/ Home work WS Geometric Sequences.
4