Question

Some sequences follow predictable patterns, though the pattern might not be immediately apparent. Other sequences have no pattern at all. Explain, when possible, patterns in the following sequences:

a. 5, 4, 3, 2, 1
b. 3, 5, 1, 2, 4
c. 2, 4, 3, 5, 1, 5, 1, 5, 1, 5, 1, 7
d. S, M, T, W, T, F, S
e. 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31
f. 1, 2, 3, 4, 5, ..., 999, 1000
g. 1, -1, 1, -1, 1, -1, ...
h. 4, 7, 10, 13, 16, ...
i. 10, 100, 1000, 10000, , ...

Answer 1

each number equals a triangular number plus 1. As the third column of Bernoulli's triangle (k = 2) is a triangular number plus one, it forms the where n ≥ 2. 1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191, 211,