How can I predict the last element of the fixed length=8 sequence after I get each element?
This can be modelled as a Markov Chain.
Let us say each element in your list can take N states. You can then represent a first order markov chain by build an N x N matrix - where each cell represents a state transition probability.
You can use this state transition probability to predict the most likely value X9 takes based on the known value from the previous timestep X8.
You also have the option of using a higher order markov chain - for e.g. a second order chain could allow you to predict X9 based on values from the previous 2 timesteps - X7 and X8.