1. Linear Sequences Slideshow 7, Room 307 Mr Richard Sasaki, Mathematics Slideshow 7, Room 307 Mr Richard Sasaki, Mathematics

2. Find patterns in sequencesFind patterns in sequences Make formulae for sequences (the n-th term)Make formulae for sequences (the n-th term) Use formulae to find positions of certain numbersUse formulae to find positions of certain numbers Objectives First, please try the 5 minute vocabulary check. The purpose of this is to not fall for decoy information, good luck!

3. Answers 5 5 240 Yen 5 7 4 3 15 (or 12) 1050ml 5 (naan bread and tandoori chicken)

4. Sequences A sequence is an ordered number pattern. It is often easy to see which numbers are missing in the pattern or the next numbers that come. 3, 5, 7, 9, __, 13, __, __ 11 15 17 Here it was easy to tell that the numbers increase by 2 every step to the right. If numbers go up (or down) in the same way every step, then the sequence is linear.

5. Sequences With sequences, it is important to understand each number’s position. 3, 5, 7, 9, __, 13, __, __ 11 15 17 1 2 3 4 5 6 7 8 20 41 Position Number

6. Sequences 3, 5, 7, 9, __, 13, __, __ 11 15 17 1 2 3 4 5 6 7 8 20 41 Position Number Let’s try to make a formula for this sequence. Is that it? Let’s check.

7. Sequences 3, 5, 7, 9, __, 13, __, __ 11 15 17 1 2 3 4 5 6 7 8 Position Number 2,4, 6, 8,10, 12, 14, 16 All of the numbers in our test are slightly off, how much by? We need to add 1 to each. Example 7, 10, 13, 16, 19, … Finished! The numbers increase by each time. 3

8. Sequences 7, 10, 13, 16, 19, … 1 2 3 4 5 Position Number A quicker way to do this is to find the 0 th term. 0 __, 4 We simply add the 0 th term to our formula. 7,10, 13, It looks good!

9. Sequences Example Find a formula for the n th term for the sequence below. Also, find out what the 50 th term is. 2, 7, 12, 17, 22, … How much do the numbers increase by? 5 What would the 0 th term be? -3, -3 What is the formula for the n th term? - What would the 50 th term be? 247

10. Answers - Easy 8 12 14 14 19 50 62 66 21 3339 -5 -3 3 2 -10 -14 2 5 8 0.5 -3 1 0 -5 1 -4

11. Answers - Medium 3 2

12. Answers - Hard 6 1216 69 4.5 5.5 -2 -5 6 74 1, 5, 9, 13, 17, 21, 25, 29