Suppose a recurrence relation
an=4an−1−4an−2
where a1=14 and a2=40
can be represented in explicit formula, either as:
Formula 1:
an=pxn+qnxn
or
Formula 2:
an=pxn+qyn
where
x
and
y
are roots of the characteristic equation.
Determine
p
and
q
.
characteristic equation:
is the only characteristic root. Therefore we know that the solution to the recurrence relation has the form
Given
Therefore the solution to the recurrence relation is
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