Algebraic, Geometric, or Neither
The numbers -1, 2, 5, 8, ... are an example of this type of sequence.
What is Algebraic?
This recursive formula describes the following sequence:
-3, 1, 5, 9, ...
What is
f(1) = -3
f(n) = f(n-1) + 4
These are first 4 terms of the sequence described by the formula
f(n) = 3 + 12(n-1)
What are
3, 15, 27, 39
The sum of the first 4 terms of the sequence described by the following formula:
f(1) = -3
f(n) = f(n-1) + 4
What is 12?
The number of students on this class.
What is 25?
The numbers 3, -9, 27, -81, ... are an example of this type of sequence.
What is Geometric
This recursive formula describes the following sequence:
216, 72, 24, 8, ...
What is
g(1) = 216
g(n) = g(n-1)/3
These are first 4 terms of the sequence described by the formula
g(n) = 9* 2^n
What are 18, 36, 74, 148
The sum of the first 4 terms of the following sequence:
g(1) = 216
g(n) = g(n-1)/3
What is 320?
The number of desks on this room.
What is 31?
The following recursive formula describes this type of sequence:
P(1) = 10,000
P(n) = 1.1 * P(n-1)
(This formula might describe the interest earned by a bank account, for example.)
What is Geometric?
This recursive formula describes the following sequence:
81, 72, 63, 54, ...
What is
f(1) = 81
f(n) = f(n-1) - 9
This explicit formula describes the geometric sequence
256, 64, 16, 4, ...
What is g(n) = 256 * (1/4)^(n-1)
The sum of the first 4 terms of the following sequence:
f(1) = 81
f(n) = f(n-1) - 9
What is 270?
This is Mr. Patterson's current favorite genre of music.
What is ska or math rock.
The following explicit formula describes this type of number sequence:
r(n) = -3 + 4n
What is Algebraic
This recursive formula describes the following sequence:
12, 18, 27, ...
What is
f(1) = 12
f(n) = (3/2) * f(n-1)
This is the explicit formula for the sequence 5, 3, 1, -1, ... that begins on term zero.
What is f(n) = 7 - 2n
The sum of the first 3 terms of the following sequence:
f(1) = 12
f(n) = (3/2) * f(n-1)
What is 46?
What is Mr. Patterson's favorite type of soda.
What is Poppi blue flavor?
You start with a square piece of paper. At step one, you cut the paper into 4 equal pieces. On the second step you divide one of the corner pieces into 4 equal pieces. On the third step you again divide one of the smallest pieces into 4 and continue on in this manner. The total number of pieces, regardless of size, is an example of this kind of sequence.
What is neither a Geometric nor an Algebraic sequence.
This recursive formula describes the following sequence:
1, 1, 2, 3, 5, 8, 13, 21, 34, ...
What is
f(1) = 1
f(2) = 1
f(n) = f(n-1) + f(n-2)
This is the explicit formula that describes the area of the following sequence of rectangles: The first rectangle is 2 by 3. The second rectangle is 3 by 4. The third rectangle is 4 by 5.
What is A(n) = (n+1)(n+2)
The sum of the first 5 terms of the following sequence:
f(1) = 1
f(2) = 1
f(n) = f(n-1) + f(n-2)
What is 12?
This number is Mr. Patterson's birthday
What is 29?