1. Sequences Arithmetic Sequence:
Is a pattern of numbers where any term (number in the sequence) is determined by adding or subtracting the previous term by a constant called the common difference.
Example:
2, 5, 8, 11, 14, ____, ____, ____
Common difference = 3
Geometric Sequence:
Is a pattern of numbers where any term (number in the sequence) is determined by multiplying the previous term by a common factor.
Example:
2, 6, 18, 54, 162, _____, _____, ____
Common Factor = 3

2. Examples of Geometric Sequence
1. Starting with the number 1 and using a factor of 4, create 5 terms of a geometric sequence.
1 , 4 , 16 , 64 , 256
2. Starting with the number 2 and using a factor of 5, create 5 terms of a geometric sequence.
2 , 10 , 50 , 250 , 1250
3. Starting with the number 5 and using a factor of 3, create 5 terms of a geometric sequence.
5 , 15 , 45 , 135 , 405
4. In the geometric sequence 2, ____, 72, 432, .Find the missing term. 12 12
5. In the geometric sequence 6, ____, 24,... Find the missing term.

3. Formula for nth term of a Geometric Sequence

4. You Try

5. Geometric Mean
A term between two terms of a geometric sequence is the geometric mean of the two terms.
Example:
In the geometric sequence 4, 20, 100, ….(with a factor of 5), 20 is the geometric mean of 4 and 100.
Try It:
Find the geometric mean of 3 and 300.
3 , ___ , 300 30

6. Geometric Mean : Fact
Consecutive terms of a geometric sequence are proportional.
Example:
Consider the geometric sequence with a common factor 10.
4 , 40 , 400
(4)(400) = (40)(40)
cross-products are equal
1600 = 1600

7. Therefore ……….. To find the geometric mean between 7 and 28 ...
label the missing term x
7 , ___ , 28
write a proportion
cross multiply
solve

8. The geometric mean between two numbers a and b is the positive number x where . Therefore x = .
Try It:
Find the geometric mean of . . .
Answer = 20
and 40
2. 1 and 36
Answer = 6
and 20
Answer = 14.14
4. 5 and 6
Answer = 5.48
and 12.2
Answer = 9.94