About the sequence: $1, 3, 8, 24, 29, 87, 92, ?...$ find $a_n$ This is a classic and curious recurrence sequence used in logic tests. Your rule can be determined as follows:
for $n$ even: $a_n = 3a_{n-1}$
for $n$ odd: $a_n = a_{n-1} + 5$
That is, the ratio alternates with each term.
Will there be a single formula for $a_n$ in terms of $n$?

For an even value
\begin{eqnarray*}
a_{2n}=3a_{2n-1}=5+3 a_{2n-2}.
\end{eqnarray*}
Iterate this
\begin{eqnarray*}
a_{2n}=5+3\times 5 +3^2 \times 5 + \cdots 3^{n-1} \times 5 +3^n.
\end{eqnarray*}
Sum the geometric series 
\begin{eqnarray*}
a_{2n}=5\frac{3^{n}-1}{3-1}+3^n = \frac{7 \times 3^n -5}{2}.
\end{eqnarray*}
