Math Plus Fun, Number Sequences - UCSB
Number Sequences
A common math problem gives you a sequence of 3 or more numbers and asks you to guess the next number, or the next two numbers, in the sequence.
1 2 3 4 ? Add 1 to a number to get the next one
0 2 4 6 ? Add 2 (even numbers)
1 3 5 7 ? Add 2 (odd numbers)
5 15 25 35 ? Add 10
22 19 16 13 ? Subtract
90 82 74 66 ?
1 2 4 8 ? Multiply
2 6 18 54 ?
81 27 9 3 ? Divide
64 32 16 8 ?
5 4 6 5 7 6 8 ? Subtract 1, add 2
0 1 3 7 ? Multiply by 2 and add 1
1 4 9 16 ? Squares
1 1 2 3 5 8 ? Add the previous two numbers
1 2 2 4 8 32 ? Multiply previous two numbers
Not all sequences are obtained by arithmetic operations:
2 3 5 7 11 ? Prime numbers
2 3 5 6 7 8 10 All numbers, except squares
1 4 7 11 14 ? Numbers formed by straight lines
Sequences can be formed by shapes and other things beside numbers
[pic]
[pic]
O T T F F S S ? First letter of numbers
J F M A M J ? First letter of months
[pic]
[pic]
Do sequences have meanings? Many sequences in which mathematicians are most interested do have meanings or appear in nature.
Example 1: Odd numbers
1 3 5 7 9 11 13 15 17 . . .
[pic]
Example 2: Squares
1 4 9 16 25 36 49 64 81 . . .
[pic]
Example 3: Doubling sequence
1 2 4 8 16 32 64 128 256 . . .
Family tree: 1 you, 2 parents, 4 grandparents, 8 great grandparents, and so on
Example 4: Fibonacci sequence
1 1 2 3 5 8 13 21 34 . . .
Add the previous two numbers to get the next number
Family tree for a bee (male bee or drone has a mom, female bee has both mom and dad)
Number of petals in flowers
[pic] [pic] [pic] [pic]
White Calla Lily (1) Euphorbia (2) Trillium (3) Columbine (5)
[pic] [pic] [pic] [pic]
Bloodroot (8) Black-eyed susan (13) Shasta daisy (21) Field daisy (34)
[pic]
-----------------------
?
?
?
?
My Family Tree
My family tree,
if I were a boy bee
Myself
My family tree,
if I were a girl bee
Mom
Dad
Mom
Dad
Dad
Mom
Dad
Mom
Dad
Mom
Dad
Mom
Dad
Mom
Dad
Mom
Dad
Mom
Mom
Mom
Dad
Mom
Dad
Mom
Dad
Mom
Dad
Mom
Mom
Mom
Myself
(Boy)
Myself
(Girl)
................
................
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