Sequences – Linear and Quadratic

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.

mathsinnit

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.

MATHSINNITBOI

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.

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s