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## Homework Statement

Let d

_{0}, d

_{1}, d

_{2},... be defined by the formula d

_{n}= 3

^{n}- 2

^{n}for all integers n ≥ 0. Show that this sequence satisfies the recurrence relation.

d

_{k}= 5d

_{k-1}- 6d

_{k-2}.

## Homework Equations

## The Attempt at a Solution

I found that d

_{k}= 3

^{k}- 2

^{k}

d

_{k-1}= 3

^{k-1}- 2

^{k-1}

d

_{k-2}= 3

^{k-2}- 2

^{k-2}

after plugging d

_{k-1}and d

_{k - 2}into the formula d

_{k}= 5d

_{k-1}- 6d

_{k-2}, i am stuck and do not understand how to do the algebra if that is what i 'm supposed to be doing...any help?