Algorithm for creating a sequence over multiple values?

Question

Algorithms

There is such a thing in Excel, when you fill in 2 cells, and then select them and drag them down, let's say, values ​​are generated for the following cells. It is necessary to implement something similar, a quick Google search does not give an answer, maybe I’m scoring the wrong keywords. I don’t ask for a ready-made solution, tell me an article that describes the algorithm and the most common filling options. Thank you.

Answer 1

planetcalc.ru/177 (arithmetic progression)
planetcalc.ru/4193 (geometric progression)
All formulas are described there.

Answer 2

If you need a linear sequence over two values, then everything is simple:
k = N1 - N0
Ni = N0 + k*i

Answer 3

First, determine the function, for example, using the least squares method, or set it manually (as in the neighboring answers, but nothing else can be done with two points), and then extrapolate.