Five different types of sequences include the Natural Numbers sequence (1, 2, 3...), which is an infinite sequence that continues indefinitely. Another is the Triangular Numbers sequence (1, 3, 6, 10...), where each term is the sum of natural numbers up to its position, given by the explicit formula $t_n = \frac{n(n+1)}{2}$.

We can also have a sequence of unit fractions (1, 1/2, 1/3...), where the terms are fractions occurring in decreasing order. A fourth type is an Arithmetic Progression (AP), where each term after the first is obtained by adding a fixed number (common difference $d$) to the previous term; this can include negative integers like -7, -3, 1, 5, 9... Finally, a finite sequence has a fixed number of terms and ends, such as 6, 12, 24, 48, 96.