When you hear the word sequence, it probably calls up different thoughts in your mind. Let's define this term as used in math.
Sequence
A sequence is an ordered list or an ordered set of numbers.
This order has specific rules that tell you how to figure out each number of the sequence.
Arithmetic Sequence
An arithmetic sequence follows a specific pattern where a number is added to get from one term to the next. This number is fixed and is called the common difference, denoted by the letter d.
The sequence is made up of terms, a1, a2, a3, and so on. To get from one term to another, you add the common difference.
So, for example
a1 + d = a2
a2 + d = a3
a3 + d = a4
The tabs below show some examples of sequences and how they work.
Sequence 1
Sequence 2
0, 3, 6, 9, 12, 15, ...
This is an arithmetic sequence with a common difference of 3. To get from one term to the next, you need to add 3.
0 + (3) = 3
3 + (3) = 6
6 + (3) = 9
To find the common difference, you could subtract the current term minus the previous term.
For example:
12 - 9 = 3
or
15 - 12 = 3
The dots at the end mean that the sequence continues on forever following the same pattern.
10, 5, 0, -5, -10, ...
In this sequence, you add -5 to each term. You may also think of this as subtracting 5 from each term.
So the common difference in this sequence is (-5).
10 + (-5) = 5
5 + (-5) = 0
0 + (-5) = -5
