1. 11.3 – Geometric Sequences

2. What is a Geometric Sequence?
The ratio of a term to it’s previous term is constant.
This means you multiply by the same number to get each term.
This number that you multiply by is called the common ratio (r).

3. Ex: Determine if the sequence is geometric
Ex: Determine if the sequence is geometric. If so, identify the common ratio
1, -6, 36, -216
yes. Common ratio=-6
2, 4, 6, 8
no. No common ratio

4. Important Formula for Geometric Sequence:
Explicit Formula
an = a1 * r n-1
Where:
an is the nth term in the sequence
a1 is the first term
n is the number of the term
r is the common ratio

5. Ex: Write the explicit formula for each sequence
First term: a1 = 7
Common ratio = 1/3
Explicit:
an = a1 * r n-1
a1 = 7(1/3) (1-1) = 7
a2 = 7(1/3) (2-1) = 7/3
a3 = 7(1/3) (3-1) = 7/9
a4 = 7(1/3) (4-1) = 7/27
a5 = 7(1/3) (5-1) = 7/81
Now find the first five terms:

6. Explicit Arithmetic Sequence Problem
Find the 19th term in the sequence of ,33,99,
an = a1 * r n-1
Start with the explicit sequence formula
Find the common ratio between the values.
Common ratio = 3
a19 = 11 (3) (19-1)
Plug in known values
a19 = 11(3)18 =4,261,626,379
Simplify

7. Find the 10th term in the sequence of 1, -6, 36, -216 . . .
Let’s try one
Find the 10th term in the sequence of , -6, 36,
an = a1 * r n-1
Start with the explicit sequence formula
Find the common ratio between the values.
Common ratio = -6
a10 = 1 (-6) (10-1)
Plug in known values
a10 = 1(-6)9 = -10,077,696
Simplify