1. Arithmetic & Geometric Sequences
AS Maths with Liz
Core 2

2. RECAP – Arithmetic Sequences

3. Arithmetic Sequences June 2012 – Question 1

4. Working out
Use subtraction to find out how much the series is increasing by each time.
Double check that this value is consistent as you progress through the series.
The common difference is 9.

5. Working out Use the formula for finding the nth term…
Use the formula for finding the sum to n terms…

6. Arithmetic Sequences tends to infinity June 2009 – Question 3

7. Working out
Substitute in given information and solve for k.

8. Working out
We know that k = 0.75, so substitute into given formula and find 3rd and 4th term.

9. Working out
(i) To find L, simply replace and with L in your given equation.
(ii) Solve for L.

10. Geometric Sequences

11. Example 1
Solution: Use given formulae to work out the 5th term, but for this, we need to find the common ratio r and the first term a.
What do we multiply by to get from one term to the next?
What is the first term?
Formula to find the 5th term:
Formula to find the sum to 10 terms:

12. Geometric Series Sum to Infinity
In cases where the common ratio is between really small (a number between -1 and 1), the sum of the series will eventually converge on a certain value. Try the following using our formula from the previous slide….
Find
As you can see, the more terms we add on, the less and less the sum changes. It seems to be approaching Let’s skip to adding up the first 100 terms and see…
Shortcut formula if common ration is between -1 and 1:

13. You try! June 2013 – Question 1

14. Working out

15. June Question 7

16. Independent Study Announcement DUE 21ST APRIL
Finish all exam questions from handout & mark in a colourful pen
mymaths – Geometric Sequences
mymaths – Binomial Expansion
FULLY COMPLETE Core 2 June 2012 past paper. Mark in a colourful pen. This will be turned in.
DUE 21ST APRIL
Announcement
Test over ARITHMETIC AND GEOMETRIC SEQUENCES will be held on 21st April.
If your score has improved on arithmetic sequences, I will replace your existing grade.