# Choosing model to predict next value in a sequence

Background: I am currently starting to work on a Machine Learning project that might be of use in car racing.

The goal of it is to give engineers suggestions about strategies.

First thing I am trying to do is given some initial amount of test laps(for example specific driver has driven 20 warmup laps and we recorded the times taken for each of them) predict/show the distribution of probabilities for the next lap time.

The laps' times have a relatively small deviation(so far we are not taking into account pitstops).

I have read several articles, blog entries and answers on StackExchange for predicting next value in a sequence. Answers vary and (possibly due to me being rather a layman in ML and Stats) suggest different things with some of them suggesting to build an RNN or try various things and check which works best. However, implementing RNN or other ML algorithms is not an easy task, so I would prefer to have a sense of direction of where I should research.

Question(Part 1):

Given a sequence of real numbers $t_1,t_2,t_3,...,t_n$ with a relatively small standart deviation, how to predict the next value $t_{n+1}$(or the probability $P$ next value $t_{n+1}$ will be in some interval $(x,y)$ where $x\in \mathbb{R}$,$y\in \mathbb{R}$ (real numbers))?

Question(Part 2):

If there is no simple answer to the previous part, which areas of ML should I research to find the best model?

End of question.

I would be grateful if the answer was in rather simple terms, as I am a layman in Machine learning and Statistics.

Thank you.