Geometric Sequences Chapter 7

The Basics

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, ... , ...

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 = 0.5 and 10 ÷ 20 = 0.5 So r = 0.5

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

Example 1

Example 1 Solution

Example 2

Example 2 Solution

Example 3

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

The sum of a geometric series

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

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