Topic 2 - Sequences

term 1

Arithmetic sequence explicit/general rule formula

Tn=a+(n-1)d

Arithmetic sequence recursive formula

Tn+1=Tn+d , T1=a OR Tn=Tn-1 + d, T1=a

Common difference rule

d=next term-previous term

Geometric sequence explicit/general rule formula

Tn=ar^(n-1)

Geometric sequence recursive formula

Tn+1=Tnr , T1=a

Growth rule

r>1

Decay rule

0<r<1

First order recurrence relation formula

Tn+1=rTn+d

Diverging sequence rule

b≥1 or b≤-1

Steady State value

For −1 < 𝑏 < 1, the terms of a first order linear sequence will approach a single value as term number (𝑛) increases. The sequence is said to be converging on a long term steady state value.

Converging sequence rule

-1<b<1

Steady state rule

Tn+1=Tn=T