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

3 7 11 15 19 These are the first 5 terms of a sequence 3 7 11 15 19 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 = 11 t4 = 15 t5 =19

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

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

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

To find the general rule describing a sequence Example: 3 7 11 15 19 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

To find the general rule describing a sequence Example: 3 7 11 15 19 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

To find the general rule describing a sequence Example: 3 7 11 15 19 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