Sequences

Recursive rule

A recursive rule generates the next term of a sequence by using the previous term or terms.

First order recursive rule

Uses only one existing term to generate the next term.

Second order recursive rule

Uses the previous two terms to generate the sequence.

Term before nth term

Tn-1

Term after nth term

Tn+1

Arithmetic sequence

Sequence obtained by adding or subtracting a constant number from the previous term.

Common difference

The difference between consecutive terms of an AP

Geometric sequences

Multiplying the previous term by a fixed number called a common ratio, r.

Common ratio found by…

Tn+1/Tn

General rule

• Find the nth term using n

• Allow you to jump to any term number

General rule AP

Tn=a+d(n-1)

General rule GP

Tn=a x r^(n-1)

First order linear relation

Tn+1=rTn+d, T1=a

Steady state

d/1-r