Number series can have general term 2^(2^n) + 1, for n = 0, 1, 2, ... {Fermat's numbers} {Fermat numbers}.
Fibonacci sequences have consecutive-number ratios that approach golden section, (1 + 5^0.5) / 2 {Fibonacci ratio}.
pi = 4 * (1 - 1/3 + 1/5 - 1/7 + 1/9 - ...) {Gregory's series} {Gregory series}.
Arithmetic progression can have first term one and common difference n - 2, where n is number of polygon sides {polygonal number}.
n can be three, so sequence is 1, 3, 6, 10, 15, 21, ... {triangular number}.
n can be four, so sequence is 1, 4, 9, 16, 25, ... {square number, polygonal}.
n can be five, so sequence is 1, 5, 12, 22, ... {pentagonal number}.
For n, sequence is l, n, 3*n - 3, 6*n - 8, ... {n-gonal number}.
general
In general, 0.5 * (r + 1) * (r*n - 2*r + 2), where r is whole number, makes polygonal numbers.
Outline of Knowledge Database Home Page
Description of Outline of Knowledge Database
Date Modified: 2022.0225