The for a can be expressed as
is the of the sequence. To write the rule, r
must be found. Consider the geometric sequence
To find r,
we can divide any term with the term that comes before it. Let's use a2=6
the recursive rule can be written as
As it's written, this rule describes any sequence with a common ratio of 2.
For example, it can describe
as well as
To ensure the recursive rule defines the given sequence, it is necessary to also give the first term, a1.
Thus, the recursive rule for the given sequence is
Now that the recursive rule is known, it can be used to find any term, provided that the previous term is given. For example, since a4=24, a5
can be found.
Thus, the 5th
term in the sequence is 48.