In mathematics, numbers are often arranged in a sequence.
Often a sequence follows a rule or pattern.
Easy Sequence
Some sequences are obvious: 2, 4, 6, 8, 10... This is the sequence of EVEN numbers.
The formula for this sequence is 2n where n stands for a counting number.
To find the next number in this sequence, calculate 2 x 6 = 12
Slightly Harder Sequence
The sequence 1, 4, 9, 16, 25... is the sequence of square numbers. Comparing this sequence to the set of counting numbers {1, 2, 3, 4..}
1

2

3

4

5

...

1

4

9

16

25

...

The formula for this sequence is n^{2}^{.} The next number in this sequence is 6^{2} = 36
More Difficult Sequence
The number of diagonals in polygons forms a sequence.
Name of polygon

Triangle

Quadrilateral

Pentagon

Hexagon

Heptagon

Number of sides 
3

4

5

6

7

Number of diagonals 
0

2

5

9

14

The sequence for the number of diagonals is 0, 2, 5, 9, 14... The pattern for this sequence is an increase of 2, 3, 4 between each term. The formula for this sequence is The next number in this sequence is 20
