PAP Sequence and Series.notebook
Pre­AP Algebra 2 9.3 Geometric Sequence
*Objective: Define, identify, and apply geometric sequence
You build a geometric sequence by MULTIPLYING each term by a constant
The ratio of any term to its preceding term is a constant value
A geometric sequence with a starting value a and a common ratio r is a sequence of the form:
a, ar, ar2, ar3, ... A recursive definition for the sequence has two parts:
a1 = a
initial condition
an = an ­ 1 * r n ­ 1, n >1 recursive definition
An explicit definition for geometric sequence is a single formula:
an = a1 * r n ­ 1, n >1
Is teh sequence geometric? If so what is the common ratio?
Ex1) a. 3, 6, 12, 24, 48, ...
b. 3, 6, 9, 12, 15, ...
c. 35, 310, 315, 320, ...
Analyzing Geometric Sequences
Ex2) a. Find the 10th term of the geometric sequence: 4, 12, 36, ...
b. find the 14th term of the geometric sequence: 1, 5, 25, ...
c. find the 2nd and 3rd terms of the geometric sequence: 2, _____, _____, ­54
d. find the second and 3rd terms of the geometric sequence: 4, __, ___, 256
Using a Geometric Sequence:
Ex3) When a ball bounces, the heights of consecutive bounces form a geometric sequence. What are the heights of the 4th and 5th bounces?
To find the height of the 10th bounce, would you use the recursive or explicit formula? Why?
In a geometric sequence, the square of the middle term of any three consecutive terms is equal to the product of the other two terms.
Ex: 2, ­6, 18, ­54, ...
The geometric mean of two positive numbers x and y is √xy
There is only one geometric mean and is a possible value to fill in a geometric sequence, the opposite of the geometric mean is the other possible value.
Using the geometric mean
Ex4) a. What are possible values of the missing term of the geometric sequence: 48, ____, 3, ...
b. The 9th and 11th terms of a geometric sequence are 45 and 80. What are possible values for the 10th term?
August 26, 2015