1. 11.3
Geometric Sequences

2. Geometric Sequence Definition: The constant is called : Common Ratio
A sequence in which the all terms after the first are found by multiplying the by a constant
2, 4, 8, 16, … (multiply each term by 2)
81, 27, 9, 3, ….. (multiply each term by 1 3
The constant is called : Common Ratio

3. Find the next two terms in the sequence
405, 135, 45,….
16, 24, 36, ….

4. Geometric Sequence Formula: an=a1rn-1
0.05, 0.25, 1.25, 6.25, …
r = =5, =5, =5
an = (.05)5n - 1

5. Find a term given the first term and the common ratio
a1 = r = -2
Find the eighth term
a1 = − r = 3
Find the sixth term

6. Write an equation for the nth term
432, 72,12, ….

7. Write an equation for the nth term
72, 56, 40, 24, …

8. Find a term given one term and the common ratio
a4 = r = 3
Find the tenth term.
aA3 = r = 4
Find the eighth term

9. Geometric Means
The terms between any two non-successive terms in a geometric sequence
Use the formula to find the common ratio
Then use the common ratio to calculate the geometric means

10. Find the geometric means
2.25, __, __, __, 576
Find the two geometric means between 4 and 13.5