CalcBC
Chp 11-2 Series (Geometric)
NOTES
1.
SEQUENCES
SEQUENCE – ordered list of numbers,
a
1
,
a
2
,
a
3
,
a
4
,
…
, a
n
Sequences are organized by three categories:
arithmetic, geometric, and neither
ARITHMETIC SEQUENCE – sequence formed by adding the same amount
to each term
Ex(arithmetic)--
2,
5,
8,
11,
14,
17,
…
Ex(not arithmetic)--
2,
5,
8,
12,
15,
18,
…
What is the COMMON DIFFERENCE?
No common difference.
3 is the common difference because it
No common difference because 3 is added for some
is the amount added to each term to get
terms
and
4 is added for one of them
the next term.
GEOMETRIC SEQUENCE -- sequence formed by multiplying the same amount
to each term
Ex(geometric)--
2,
−6,
18,
−54,
162, − 486,
…
Ex(not geometric)--
2,
6,
18,
54,
108,
324,
…
What is the COMMON RATIO?
No common ratio.
3 is the common ratio because it
No common ratio because 3 is multiplied for some
is the amount multiplied to each term
terms
and
2 is multipled for one of them
to get the next term.
Ex(geometric)--
a,
ar,
ar
2
,
ar
3
,
ar
4
,
…
Ex(geometric)--
8,
4,
2,
1,
½ ,
¼ ,
,
…
What is the common ratio?
_______
What is the common ratio?
_______
What are the next two terms?
______________
What are the next two terms?
______________
GEOMETRIC SEQUENCES have a predictable general term.
EXPLICIT FORMULA for the GEOMETRIC GENERAL TERM: