General Terms

Generals Terms

MathsDirect

A sequence of numbers, is simply a list of numbers, generated by some rule.

For example.

Each term in a sequence can be referred to by it's place in the sequence,

i.e. first term, third term, n^thterm.

In the above sequence, the 4^thterm is 12.

The rule used to generate a sequence, is often described by referring to the n^thterm. For example

So the 4^thterm is 8-1=7

Example, what is the n^thterm of

2, 8, 18, 32

The terms can be broken up as

which is the same as

so the n^thterm is

A sequence can develop in 4 ways.

Divergent

The terms keep growing

Convergent

The terms converge on a single value, in this case 0.

Periodic

The sequence repeats itself after a set number of terms.

Oscillating

The sequence oscillates between 2 values.