patterns and sequences
arithmetic sequence
sequence whose consecutive terms have a common difference
for example: 3, 5, 7, 9, ...
geometric sequence
sequence such that the ratios of consecutive terms are the same
for example: 2, 6, 18, 54, ...
arithmetic, geometric or neither?
other types
there are other sequences that aren't arithmetic or geometric
for example: 1, 4, 9, 16, 25, ...
just for fun ...
O, T, T, F, F, S, S, E, ...
J,F,M,A,M, ...
George, John, Thomas, James, ...
Martha, Abigail, Martha, Dolly, ...
George, Thomas, Abe, Alexander, ...
Aquarius, Pisces, Aries, Taurus, ...
M, V, E, M, ...
AL, AK, AZ, AR, ...
H, He, Li, Be, ...
3, 8, 13, 18, 23, . . .  
24, 12, 6, 3, 3/2, 3/4, . . .
2, 5, 10, 17, . . .  
1, 2, 4, 8, 16, . . .
55, 51, 47, 43, 39, 35, . . .
1, 4, 9, 16, 25, 36, . . .
3, 9, 27, ...
Arithmetic or Geometric?
Find the next three terms.
Find the 10th term. 
Find the 100th term.
Find the sum of the first 30 terms.
12, 10, 8, 6, ...
Arithmetic or Geometric?
Find the next three terms.
Find the 10th term.
Find the 100th term.
Find the sum of the first 30 terms.