emathematics.net
Español
User: desconectar
 
Maths Exercices
Recursion Sequences

A recursive sequence is an ordered list of numbers defined by a starting value and a rule. You generate the sequence by applying the rule to the starting value, applying the rule again to the resulting value, and then repeating this process.

A recursive formula always has two parts:
  1.  the starting values.
  2.  the recursion equation for an as a function of the terms before it.

1, 1, 2, 3, 5, 8, ... is a recursive sequence, where:

a1=1
a2=1
an=an-1+an-2

(It is well known as The Fibonacci Sequence)

Given:
a1=1
a2=2
an=2an-1+an-2

Find the next three terms.

a3=2a2+a1=2(2)+1=5

a4=2a3+a2=2(5)+2=12

a5=2a4+a3=2(12)+5=29