# Converting an Arithmetic Series to Sigma Notation

I've been struggling with the following problem for quite a while now, and have been unable to identify a pattern;

You have a geometric series $$Y$$ for which we have the following rule: $$Y_{t+1} = \beta_0 + \beta_1 Y_t + \beta_2 Y_{t-1}.$$

All beta variables ($$\beta_0$$, $$\beta_1$$, and $$\beta_2$$) are constants, while $$Y_t$$ and $$Y_{t-1}$$ are the first and second lags of $$Y_{t+1}$$. Find an expression for $$Y_{t+h}$$ as a function of $$Y_t$$ and $$Y_{t-1}$$ using finite sigma notation.

If anyone can offer any advise about how I would go about solving it, I would be very grateful.