Investigation: Mathematical Patterns

Note that series near the bottom are quite difficult.
Answers:
a) Each number increases by 3 over previous
1, 4, 7, 10, 13, 16, 19, 22

b) Each number increases by 8 over previous
5, 13, 21, 29, 37, 45, 53, 61

c) Each number increases by 4 over previous
11, 15, 19, 23, 27, 31, 35, 39

d) Each number increases by 7 over previous
3, 10, 17, 24, 31, 38, 45, 52

e) Each number increases by 9 over previous
5, 14, 23, 32, 41, 50, 59, 68

f) Each number increases by 2 over previous
6, 8, 10, 12, 14, 16, 18, 20

g) Two successive integers, skip one integer, two successive integers, etc.
1, 2, 4, 5, 7, 8, 10, 11

h) Up 6, back 3, up 6, back 3, etc.
3, 9, 6, 12, 9, 15, 12, 18

i) Binary series. Each number doubles previous.
1, 2, 4, 8, 16, 32, 64, 128

j) Interval between numbers increases by one for each step.
1, 2, 4, 7, 11, 16, 22, 29

k) Alternate numbers increase by 11, which increments both digits. In-between numbers reverse the digits of the previous number, and they also increase by 11. The series only works for two-digit numbers.
51, 15, 62, 26, 73, 37, 84, 48

l) Fibonacci series. Each number (after the first two) is the sum of the two previous. The Fibonacci series describes the spiral growth in seashells and other geometric growth in nature.
0, 1, 1, 2, 3, 5, 8, 13
(The next numbers: 21, 34, 55…)

m) Factorial series. Each number is the product of successive integers. For example, the fourth number is 4! (4 factorial) = 4 x 3 x 2 x 1 = 24,
the fifth is 5! = 5 x 4 x 3 x 2 x 1 = 120, etc.
1, 2, 6, 24, 120, 720, 5040, 40320