Recall that we can express a relationship algebraically using an equation.
recursive equation
Practice makes perfect
As the exercise mentions, a recursive rule defines a sequence by giving the first term or terms. Furthermore, it tells how the next term is related to the previous term or terms. This relationship can be written algebraically as an equation which is known as the recursive equation. An example is shown below.
Example initial terms
a_1=1 and a_2=2 [1.2em]
Recurisive Equation
a_n = (a_(n-1))(a_(n-2)) [1.2em]
Sequence
1 ,2, 2, 4, 8, 32, 256 ...
With this in mind, we can complete the exercise's sentence.
A recursive rule gives the beginning term(s) of the sequence, and a recursive equation tells how a_n is related to one or more preceding term.
