Geometric Sequences.notebook
geometric sequence ­ pattern formed by multiplying each term in the sequence by a fixed number to find the next term
common ratio ­ the fixed number used to find the terms
2. 750, 150, 30, 6,...
Find the common ratio and the next term(s) :
1. 1, 3, 9, 27, ___
CR:
2. 120, ­60, 30, ___, ____
CR:
3. 1.1, 2.2, 4.4, 8.8, ___, ___
CR:
Recall: An arithmetic sequence is when you add by a fixed number
Arithmetic or Geometric?
1. 2, 4, 6, 8, ...
2. 56, 28, 14, 7, ...
Pull
Find the common ratio
1. ­3, ­6, ­12, ­24,...
Pull
Geometric
Sequences
February 15, 2017
to find common
divide a term b
previous ter
always state wh
multiplying by, n
Geometric Sequences.notebook
February 15, 2017
Finding a formula
EX: Find the fifth term of a sequence
when the first term is 5 and the
common ratio is ­2
A(5) = 5(­2)5­1
= 5(­2)4
= 5(16)
= 80
2(3)1
2(3)2
2(3)3
nth term
first term
common ratio
Find the 20th term of the previous sequence.
Pull
A(n) = a(r)n­1
A(n) = a(r)n­1
Pull
Sequence: 2, 6, 18, 54,...
Find a function rule
Let n = term number in the sequence
Let A(n) = value of the nth term
What's the pattern?
A(1) = 2
2(3) A(2) = A(3) = 2(3)(3)
A(4) = 2(3)(3)(3)
A(n) = 2(3)n­1
General Formula for Geometric Sequence
­2,621,440
Geometric Sequences.notebook
You drop a rubber ball from a height of 1m and it bounces back to lower and lower heights. Each curved path has 80% the height of the previous path. Write a rule for the height of each successive path. What height will the ball reach at the top of the fifth path?
Pull
A(n) = a(r)n­1
A(5) = 100(.8)4
A(5) = 40.96cm
Mini­Challenge
February 15, 2017