What do you call a sequence which depends on past terms?

Question

A sequence like the fibonacci sequence depends on its previous terms, I know how to write the formulae for these equations but can't remember the name.

Answer 1

A sequence is a set of numbers arranged in a one-to-one correspondence with the positive integers 1,2,3,..., and determined according to some rule. The numbers of the set constituting the sequence are called the terms of the sequence.

The sequence is usually denoted by a1,a2,a3,...., an, ..., where an or {an} is the nth term of the sequence and is a function of n. For example if {an} = (n^2+n)/2, and if we put n = 1,2,3,4..., we get for the first few terms of the sequence 2,5/2,10/3,17/4,...

If {an} = (-1)^n X1/n^2, the first few terms are -1,1/4,-1/9,1/18,-1/25,...

For the indicated sequence 1/2, -2/3,3/4,-4/5,..., the simplest general for {an} is (-1)^(n+1) X n/(n+1).

So sequences depend on {an} which is the rule for determining the nth term.

If you have a sequence where a new term is dependent on the previous few terms, then the sequence is said to be recursive. The Fibonacci sequence is an example of this case.

Answer 2

You call such a sequence recursive.

Answer 3

I think you mean a 'recursion' ☺

Doug