One of the important types of patterns in mathematics is sequences of numbers--lists of numbers where you can tell what the next number is if you know the rule.
Let me give you a few examples.
Rule | Sequence |
Add 1 to the previous number | 1, 2, 3, 4, 5, . . . |
Write only the odd numbers | 1, 3, 5, 7, 9, . . . |
Multiply the previous number by 2 | 1, 2, 4, 8, 16, . . . |
Add 3, then subtract 1, then repeat | 1, 4, 3, 6, 5, . . . |
Being able to discover patterns is an important part of mathematics and a useful skill in almost any job.
A. (This is about as easy as they come): 1, 1, 1, 1, 1, . . .
B. (This is similar to one of the examples): 1, 4, 7, 10, 13, . . .
C. (For this one, look at the differences between the numbers in the sequence): 1, 2, 4, 7, 11, 16, . . .
D. (This is a famous sequence, called the Fibonacci numbers. To find the rule for it compare each number with the two numbers preceding it.):1, 1, 2, 3, 5, 8, 13, . . .
E. (To find the rule for this one, compare each number to the positive integers (counting numbers)):1, 4, 9, 16, 25, 36, . . .
F. (It may be useful to write out the numbers one, two, three, and so on.): 3, 3, 5, 4, 4, 3, . . .
G. (Try Roman numerals -- e.g. I, II, III, IV, V etc. --to get started on this one): 1, 2, 3, 3, 2, 3, . . .
H. (This one is called the E-ban numbers. The name is a hint. Again write out the numbers one, two, etc. and compare those included with those excluded.) 2, 4, 6, 30, 32, 34, 36, 40, . . .
Finally some very important sequences:
J. Sequences can include fractions: 2, 1, 1/2, 1/4, 1/8, 1/16, . . .
K. and decimals (You may have to look this up to find the next numbers in the sequence): 3, 3.1, 3.14, 3.141, 3.1415, 3.14159, 3.141592, 3.1415926, . . .