1. Geometric Sequences
Part 1

2. Geometric Sequences
A geometric sequence is a sequence that is found by multiplying the previous term by the same number repeatedly.
The number that you multiply by is called “r”, the common ratio.
Remember that dividing is the same as multiplying by a fraction.
60 ÷ 3 = 20
60 * = 20

3. Geometric Sequences Find the common ratio for the geometric sequence
5, 20, 80, 320, …
r = 4
1, -3, 9, -27, …
r = -3

4. Geometric Sequences
Find the common Ratio for the following geometric sequences…..
320, 80, 20, 5, …
r = 1 4
5000, 5500, 6050, 6655, …
r = 1.1 or 11/10

5. Geometric Sequences Write the first 5 terms of the geometric sequence.
Remember that a geometric sequence is found by multiplying the previous term by the common ratio.
a1 = 4, r = 2
4, 8, 16, 32, 64
a1 = 9, r = -5
9, -45, 225, -1125, 5625
a1 = 8, r = 1 2
8, 4, 2, 1, 1 2
a1 = 6, r =
6, -2, 2 3 , − 2 9 , 2 27

6. Geometric Sequences
Finding the general term of a geometric sequence is done by using the formula:
an = a1 • rn-1
a1 is the first term in the sequence
r is the common ratio
n is the term number
The great thing about sequences is that everything still means the same!!

7. Geometric Sequence
Write the formula for the nth term of the geometric sequence.
an = a1 • rn-1
a1 = 8, r = 3
an = 8 • 3n - 1
a1 = -4, r = -5
an = -4 • (-5)n-1
a1 = 2, r = 1 4
an = 2 • ( 1 4 )n - 1