1. Geometric Series Overview. Finding a geometric sum eg S10
Finding the first term ‘a’
Finding the term number ‘n’
Application problems 1 2

2. Geometric Series Rule x5 S10 = ?
Start
Geometric Series Rule x5
r = common ratio = 5
Sn = …
a = first term = 1
S10 = ?
Sn = sum of the first ‘n’ terms in the sequence

3. Finding a Sum Find S12 6, 30, 150, 750... Start General Rule: Find ‘a’
Find ‘r’
Find the Sum if the first 12 terms by substituting in a = 6 n = 12 and r = 5

4. Finding a term given ‘a’
Start
Find the first term given a geometric series S12 = , and a common ratio r = 2
Substitute in n = 12, S12 = & r = 2
Simplify
Solve

5. Finding the term number ‘n’
Start
Find when the sum of a geometric sequence is first greater than 1300, (given a first term of 12, & common ratio of 1.1 )
Substitute in r = 1.1,
Sn = & a = 12
Rearrange the equation to find ‘n’
Use Logs to find n

6. An Application Problem A
Start
Egor the alligator walks 380m on day 1 of his exercise programme. Each day he gets more and more tired, so he walks 15% less than the previous day
First term = 380 m
So a = 380
1) What was his total distance walked in the first 10 days?
Substitute in a = 380, r = 0.85
A 15% decrease means multiply by 0.85 So r = 0.85
Brackets on the bottom can help

7. An Application Problem B
Start
Egor the alligator walks 380m on day 1 of his exercise programme. Each day he gets more and more tired, so he walks 15% less than the previous day
2) If he continued his exercise programme forever, how far would he walk altogether?
Sum to infinity problem
Substitute in a = 380, r = 0.85

8. The end
Note: No crocodiles or alligators were harmed during the making of this PowerPoint.