Definition §

Arithmetic Sequence / Relations

A Sequence where each term has a common difference, e.g. each term increases by 5 each time. It can also a First Order Linear Recurrence Relation It is linear when plottoned on a graph

(Explicit) Arithmetic Sequence / Relation Formula §

Where: is a Absolute Value () is the Difference Alternative Formula for Difference:

If should =

Then use the alternate formula without the e.g.

(First-Order Recurrance) Arithmetic Sequence / Relation Formula §

Where: is the First Value () is the Common Difference if it’s constant, it’s increasing, it’s decreasing

First Order Arithmetic Sequence Notes

• D > 0 : Increasing Sequence
• D < 0 : Decreasing Sequence
• D = 0 : Constant Sequence

• The Recurrance relation for any arithmetic sequence , may be written in the form: ,

this is another way of wirtiing the exact same Explicit Arithmetic Sequence formula;