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We can give a closed formula for the \(n\)th term of each of these sequences. The first is just \(a_n = -1\text{.}\) The second is \(a_n = 2^{n+1}\text{.}\) The sequence we are interested in is just the sum of these, so the solution to the recurrence relation is

\begin{equation*} a_n = 2^{n+1} - 1\text{.} \end{equation*}
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