Transcript Find the next 3 terms or missing terms for each, then write the rule in words, and the equation: 1. 3, 12, 21,

Find the next 3 terms or missing terms for each,
then write the rule in words, and the equation:
1.
3, 12, 21, …
2.
20, ___, ___, -7
3.
2, 4, 8, …
CCGPS Alg
2/20/2013
UNIT QUESTION: How do we graph
functions, and what can be done to
change the way they look?
Today’s Question:
How do we write the function to
represent a sequence?
CCGPS Alg
2/20/2013
(I.N. p71)
MCC9-12.F.BF.2 Write arithmetic
and geometric sequences both
recursively and with an explicit
formula, use them to model
situations, and translate between the
two forms.
Arithmetic Sequence
A sequence of terms that
have a common difference
between them
Geometric Sequence
A sequence of terms that
have a common ratio
between them
Explicit Formula
Formula used to find the
term of a sequence
th
n
Explicit Formula for
Arithmetic Sequence
an  a1   n  1 d
Explicit Formula for
Geometric Sequence
an  a1  r 
n1
Arithmetic or Geometric?
Example:
-22, -15, -8, -1, …
Arithmetic
d=7
Arithmetic or Geometric?
Example:
7, 4, 1, -2, -5
Arithmetic
d = -3
Arithmetic or Geometric?
Example:
256, 64, 16, 4, …
Geometric
r = 1/4
Arithmetic or Geometric?
Example:
8 16 32
4, , , ,...
3 9 81
Geometric
r = 2/3
Find the common difference, the
explicit formula, and the tenth term.
3, 9, 15, 21, …
d=6
an  a1   n  1 d
an  3   n  16
an = 6n – 3
a10  6 10  3
a10 = 57
Find the common ratio, the explicit
formula, and the seventh term.
3, 1.5, 0.75, 0.375, …
an  a1  r 
n1
an  3  0.5 
1.5
r
 0.5
3
n1
a7  3  0.5 
71
a7  0.0456875
The fifth term is 1,792. The constant
ratio is 4. Write the explicit formula.
a5  1792 and n  5 and r  4
an  a1  r 
n1
1792  a1  4 
5 1
7  a1
an  7  4 
n1