ARITHMETIC SEQUENCE

 

What is a Sequence?

A Sequence is a set of things (usually numbers) that are in order.

Infinite or Finite

If the sequence goes on forever it is called an infinite sequence,
otherwise it is a finite sequence

Examples:

{1, 2, 3, 4 ,...} is a very simple sequence (and it is an infinite sequence)

{20, 25, 30, 35, ...} is also an infinite sequence

{1, 3, 5, 7} is the sequence of the first 4 odd numbers (and is a finite sequence)

{4, 3, 2, 1} is 4 to 1 backwards

{1, 2, 4, 8, 16, 32, ...} is an infinite sequence where every term doubles

{a, b, c, d, e} is the sequence of the first 5 letters alphabetically

{f, r, e, d} is the sequence of letters in the name "fred"

{0, 1, 0, 1, 0, 1, ...} is the sequence of alternating 0s and 1s (yes they are in order, it is an alternating order in this case)

Arithmetic sequence

Before talking about arithmetic sequence, in math, a sequence is a set of numbers that follow a pattern. We call each number in the sequence a term.

For examples, the following are sequences:

1, 4, 7, 10, 13, 16, 19, .......

70, 62, 54, 48, 40, ...............

An arithmetic sequence is a sequence where each term is found by adding or subtracting the same value from one term to the next. We call this value "common sum" or "common difference"

Looking at 1, 4, 7, 10, 13, 16, 19, ......., carefully helps us to make the following observation:

As you can see, each term is found by adding 3, a common sum to the previous term

Looking at 70, 62, 54, 46, 38, ...............carefully helps us to make the following observation:

This time, to find each term, we subtract 8, a common difference from the previous term

Many arithmetic sequences can me modeled with an algebraic expression