Difference {common difference} between consecutive sequence terms can be constant {arithmetic progression}. General term is a(n) = a(1) + d * (n - 1), where d is common difference. First-n-terms partial sum is n times average of first and last terms: Sn = n * (a(1) + a(n)) / 2, where a(k) is general term, and n is number of terms.
Consecutive sequence-term ratios {common ratio} can be constant {geometric progression}. General term is a(n) = a(1) * r^(n - 1), where r is common ratio, and n is number of terms. Partial sum is Sn = a(1) * (1 - r^n) / (1 - r), where r is common ratio, and n is number of terms.
Difference between reciprocals of successive sequence terms can be constant {harmonic progression}. General term a(n) is 1 / a(n) = 1 / (a(1) + d * (n - 1)), where d is difference.
Outline of Knowledge Database Home Page
Description of Outline of Knowledge Database
Date Modified: 2022.0225