1. Geometric Sequences
Chapter 7

2. The Basics

3. Find the next two terms...
2, 4, 8, 16, ... , ...
5, 15, 45, 135, ... , ...
1, 10, 100, 1000, ... , ...
1000, 500, 250, 125, ... , ...
400, 100, 25, 6.25, ... , ...
100, 10, 1, 0.1, ...
195533, 15041, 1157, 89, ... , ...

4. For any geometric sequence
You multiply by a COMMON RATIO (r) to get from each term to the next
What is the value of r in these sequences:
10, 60, 360, 2160, ...
40, 20, 10, 5, ...
60 ÷ 10 = 6 and 360 ÷ 60 = 6. So r = 6
20 ÷ 40 = and 10 ÷ 20 = 0.5
So r = 0.5

5. In general a, ar, ar2, ar3, .... , arn-1
A geometric sequence can always be written
a, ar, ar2, ar3, , arn-1
1st term
2nd term
3rd term
4th term
Nth term

6. Example 1

7. Example 1 Solution

8. Example 2

9. Example 2 Solution

10. Example 3

11. Finish for hwk due tomorrow
Example 3 Solution
Now do Ex7A Q2, 3 and Ex7B Q2, 3, 4, 5
Finish for hwk due tomorrow

12. The sum of a geometric series

13. The sum of a Geometric Series
Use when r < 1
Use when r > 1

14. Proving the formula for the sum of a Geometric series
factorise
divide