Name: ___________________________
Date: ____________ Block: _________
Mrs. Mistron
In a geometric sequence, the ratio of any term to the
previous term is constant ( you are always multiplying
by the same number to get the next term)
The constant ratio is called the common ratio!
Identify the geometric sequences:
4, 10, 18, 28, 40,…
625, 125, 25, 5, 1, …
2, 4, 6, 8,…
1, 2, 6, 24, 120, …
-4, 8, -16, 32, -64, …
81, 27, 9, 3, 1, …
RULE FOR A GEMOETRIC SEQUENCE:
The nth term of a geometric sequence with first term a1
and common ratio r is given by…
an = a1rn – 1
Example One Write the Rule given the sequence
a. 4, 20, 100, 500, …
b. 152, -76, 38, -19,…
Example Two Write the rule given the common ratio and a term
a. a4 = 12, r = 2
b. a5 = 54, r = 3
Example Three Write the rule given two terms
a. a3 = -48, a6 = 3072
b. a2 = -12, a4 = -3
The Sum of a Finite Geometric Series
The sum of the first n terms of a geometric series with
common ratio r
is…
=
The Sum of an infinite Geometric Series
The sum of an infinite geometric series with first term a1 and
common ratio r is…
S=
provided that |r| < 1. If |r| ≥ 1 there is no sum.
Example Four Find the sum of the series
Example Five Find the Sum of the Series
Example Six In 1990, the total box office revenue in the US was about $5.02From 1990
to 2003, the total box office revenue increased by about 5.9% each year. What was
the total box office revenue from 1990 to 2003?
Example Seven Repeated Decimals
Write 0.24242424… as a fraction simplified to lowest terms