Consider the following recursion: $$C_{i+1} = a \sum_{j=1}^iC_j + b$$ where $a$ and $b$ are constants.
- Can series-element $C_i$ be expressed in terms of only its index $i$, $a$ and $b$?
- In case $C_1$ = $b$, does the answer change? simplified expression?
Thanks much.