Finding an explicit formula for An in terms of n.

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  1. Let $A_{1}= 5, A_{2} = 7,$ $A_{n+1} = A_{n} + 6A_{n-1}$.

Find an explicit formula for $A_n$ in terms of $n$.

  1. Suppose $p_{n}$ is a sequence defined by $p_{1} = 0, p_{2} = 1$ & $\forall n$, $p_{n+1} = 2p_{n} - 2p_{n-1}$.

Find a formula for $p_{n}$ in terms of $n$.

How would I begin these problems?