Arithmetic Sequences

A sequence which has a constant difference between terms. The rule is linear.

Example: 1, 4, 7, 10, 13,…

(generator is +3)

Arithmetic Sequences

n t(n)

1 1

2 4

3 7

4 10

5 13

+3

+3

+3

+3 3 2t n n

Discrete

First find the generator and the n=0 term. Then write the equation:

Ex 1:

t(0) is not in the sequence! Do not include it in tables or graphs!

Working Backwards for a Rule

36, 32, 28, 24, … 1 2 3 4

40, 0

4 40t n n

– 4

Seq

uenc

es s

tart

with

n=

1 no

w!

Sequence: t(n)

Function: f(x)

Sequences v Functions

Positive Integers (sometimes 0)

Can be all Real numbers

Domain (n) =

Domain (x) =

Can be all Real numbers

Range (f(x))=

DiscreteThe Graph is

can be ContinuousThe Graph

Range (t(n)) =

Can be all Real numbers