Name:______________________________________
Date__________________ Block ______
Continue the patterns below with the next 3 numbers. What rule does each
pattern follow?
1)
5, 10, 20, . . .
2)
2, 4, 6, 8, . . .
3)
-100, -75, -50, . . .
Continue the patterns below with the next 3 numbers. What rule does each
pattern follow?
4)
5)
2, 4, 8, 16, . . .
1 1
, , 1, 2, . . .
4 2
6) -1, 4, -16, 64, . . .
Sequences
A sequence is an ordered list of numbers. Each number is called a ___________
of the sequence.
___________
sequence
_____________
sequence
each term is found
by adding the same
number to the
previous term
each term is found
by multiplying the
previous term by
the same number
8, 11, 14, 17, ...
"n + 3"
+3 +3 +3
3, 6, 12, 24, ...
x2 x2 x2
The difference between any two consecutive terms in an arithmetic sequence is
called the ______________ ______________________.
The factor between any two consecutive terms in a geometric sequence is called
the ______________ ______________.
Sometimes the arithmetic sequence looks like the term is subtracted, but it’s really
adding a negative.
Sometimes the geometric sequence looks like the term is divided, but it’s really
multiplying a fraction.
Examples:
State if each sequence is arithmetic, geometric, or neither. If the sequence is arithmetic or geometric
describe the relationship between two consecutive terms in the sequence.
1) 35, 28, 21, 14…
________________ ______________
2) 1, 3, 9, 27…..
________________ ______________
3) 2, -4, 8, -16….
________________ ______________
4) 121, 1221, 12221 …
________________ ______________
"2n"
5) -8, -6, -4, -2…
________________ ______________
6) 2, 6, 24, 120….
________________ ______________
7) What is the common ratio of the geometric sequence shown:
8) What is the 7th term of the arithmetic sequence:
8, 32, 128,
29 , 21 , 13 , 5 ,
9) Find the missing terms in the sequence 26, 33, 40, ___, 54, 61, ___, …
Write out the next three terms of the following sequences.
10) 0, 13, 26, 39 …
11) 8, 5, 2, – 1, –4 …
12) –2, –6, –18, –54 …
13) Create three sequences. One sequence must be arithmetic, one sequence must be
geometric, and one sequence must be neither. Then describe the relationship between
two consecutive terms in each of your arithmetic and geometric sequences.
Arithmetic: ________________________________________ ______________
Geometric: ________________________________________ ______________
Neither:
________________________________________