How do we find an explicit formula for the sequence $(a_i)_{i=1}^\infty$ in terms of $a_1=C$ if
$a_{i+1}=\begin{cases} a_i-13 & i \text{ even}, \\ 2a_i & i \text{ odd}.\end{cases}\quad i\ge2 \; ?$
How do we find an explicit formula for the sequence $(a_i)_{i=1}^\infty$ in terms of $a_1=C$ if
$a_{i+1}=\begin{cases} a_i-13 & i \text{ even}, \\ 2a_i & i \text{ odd}.\end{cases}\quad i\ge2 \; ?$
One approach is to define $b_i=a_{2i+1}, b_1=C, b_{i+1}=2b_i-13, a_{2i}=2b_{i-1}$