1. Aim: To be able to describe the general rule for a sequence
C/W
Sequences
16 May 2005
Aim: To be able to describe the general rule for a sequence

2. 3 7 11 15 19 These are the first 5 terms of a sequence
Each number in a sequence is called a term.
Term 1 is 3
Term 2 is 7
Term 3 is 11
Term 4 is 15
Term 5 is 19
We will use n to represent the position of the term
in a sequence and tn to represent the term.
So in this example t1 = 3 t2 = 7 t3 = t4 = 15 t5 =19

3. n 1 2 3 4 5 To find the general rule describing a sequence
Example: n 1 2 3 4 5

4. To find the general rule describing a sequence
Example: n 1 2 3 4 5
term tn 7 11 15 19
+ 4
+ 4
+ 4
+ 4

5. To find the general rule describing a sequence
Example: n 1 2 3 4 5
term tn 7 11 15 19 4n 8 12 16 20
Adding 4 each
time so
consider 4n

6. To find the general rule describing a sequence
Example: n 1 2 3 4 5
term tn 7 11 15 19 4n 8 12 16 20 -1
Adding 4 each
time so
consider 4n

7. To find the general rule describing a sequence
Example: n 1 2 3 4 5
term tn 7 11 15 19 4n 8 12 16 20 -1
Adding 4 each
time so
consider 4n

8. To find the general rule describing a sequence
Example: n 1 2 3 4 5
term tn 7 11 15 19 4n 8 12 16 20 -1
4n -1
Adding 4 each
time so
consider 4n
So the general rule for the term in position n
is given by t = 4n -1