1. Algebra n th Term

2. Algebra When we are working to find the n th term we are looking to find patterns in number sequences.

3. Algebra Look at this sequence of numbers: 5, 9, 13, 17, 21, …, …, What are the next two numbers in the sequence? 25,29,

4. Algebra What would the 10 th number be? 5, 9, 13, 17, 21, …, …, How can we know without the 8 th and 9 th numbers..? 25,29,

5. Algebra We need to be able to use the ‘place’ value of each number (the n th term) 1234567 5, 9, 13, 17, 21, 25, 29

6. Algebra Now look at each number in the sequence. What is the difference between each number? 1234567 5, 9, 13, 17, 21, 25, 29 4 44444

7. Algebra This difference tells us how much we need to multiply the n th term by. 1234567 5, 9, 13, 17, 21, 25, 29 4 44444 1x4= 4

8. Algebra But the sequence number is 5, not 4! OK, then just add 1 as well 1234567 5, 9, 13, 17, 21, 25, 29 4 44444 1x4= 44 +1= 5

9. Algebra We know n has to be multiplied by 4, add 1 Now try it on another n… 6? 1234567 5, 9, 13, 17, 21, 25, 29 4 44444 6x4= 2424 +1= 25

10. Algebra So our rule for finding any number in this sequence is… 4n + 1 1234567 5, 9, 13, 17, 21, 25, 29 4 44444

11. Algebra When answering a question is it really important to present it so that it is really clear. Draw a small table to show both the sequence and the term place values…

12. Algebra Difference between numbers is 3 Term 1 is multiplied by 3 then subtract 1 = 2 = 3n-1 4 th term 4 x 3 - 1 = 11 nth term 1234567 Sequence 25811141720 Difference 333333