## Sequences and Patterns 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 n2.
The next number in this sequence is 62 = 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