Name that Sequence! (definitions & concepts)
What is an arithmetic sequence?
A sequence that uses addition/subtraction of a common value to create the next term in the sequence.
*key word: common difference
Arithmetic, Geometric, or Neither?
1, 2, 4, 8, 16, 32, 64, 128, ...
Geometric
-3, 1, 5, 9, ___, 17, ...
13
What is the explicit arithmetic formula?
f(n)=d(n-1)+f(1)
What is a geometric sequence?
A sequence that uses multiplication/division of a common value to create the next term in the sequence.
*key word: common ratio
Arithmetic, Geometric, or Neither?
1, 4, 9, 16, 25, ...
Neither
5, 30, 180, ____ ...
1080
What is the explicit geometric formula?
f(n)=f(1)*r^(n-1)
What does f(1) represent?
the first term of a sequence
Arithmetic, Geometric, or Neither?
-6, -3, 0, 3, 6
Arithmetic
3, 11, ___ 27, 35 ...
What is the recursive geometric formula?
f(n)=r*f(n-1)
Looking at the explicit formula below for a geometric sequence, what is the ratio?
f(n)=2*3^(n-1)
r = 3
DAILY DOUBLE!
Arithmetic, Geometric, or Neither?
If the sequence is arithmetic or geometric, identify d or r.
3, 6, 12, 24, 40, 80 ...
NEITHER!
DAILY DOUBLE
___, -132, 528, -2112, 8448 ...
33
What is the recursive arithmetic formula?
*To receive FULL points, you must be able to state the conditions of a recursive formula. When is the only time you can use the recursive formula? AKA, why does the formula kind of suck?
* you can only use a recursive formula when you are looking for a term immediately proceeding a term you already know. for example, predicting the 5th term when you already know the 4th.
f(n)=f(n-1)+d
True or False: Geometric sequences can both increase and decrease.
True :)
Arithmetic, Geometric, or Neither?
If the sequence is arithmetic or geometric, identify d or r.
81, -27, 9, -3, 1, -1/3, 1/9, ..
Geometric
R=-1/3
49.5, 43, 36.5, 30, ____ , ...
23.5
Find the recursive and explicit formula for the following sequence:
49.5, 43, 36.5, 30,...
Recursive:
f(n)=f(n−1)−6.5
Explicit:
f(n)=−6.5n+56