Mathematical sequences are lists of numbers which follow a rule.

The rule for this is called the nᵗʰ term.

In the nᵗʰ term, ‘n’ represents the position in the list. For example, n+4 would make:

Postition: 1,2,3,4,5

Number: 5,6,7,8,9

As 1+4 is 5, 2+4 is 6, 3+4 is 7 and so on.

This is called a linear sequence, as the difference between each number is exactly the same each time.

However, there is another type of sequence.

With an nᵗʰ term of n², you would have:

Pos: 1,2,3,4 ,5 ,6

No.: 1,4,9,16,25,36

The difference is different each time.

However, if you work out the difference between the differences, or the second difference, you will find that it is always the same, in this case 2.

From that, you can work out the differences and thusly the numbers.

A good understanding of algebra is all that’s needed from there, as it is just an algebraic expression.

For example, 16(2n+n²) would make:

Pos: 1 ,2 ,3 ,4 ,5 ,6 ,7

No.: 48,128,240,384,560,768,1008

and so on.