standard_description: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ³ 1.
problem_activity: Problem 1
Four sequences are shown below. Which one does not belong and why?
|  $${4, 8, 12, 16, 20 ...}$$  |    $${50, 46, 42, 38, 34, ...}$$    |
|------------------------------|-------------------------------------|
| $${1, 4, 16, 64, 216, ...}$$ | $${1600, 400, 100, 25, 12.5, ...}$$ |
Problem 2
Complete each sequence by filling in the missing terms. Then identify each sequence as arithmetic or geometric and name the common difference or common ratio.
a.
$${-2}$$
,
$$4$$
, ___, ___, ___,
$${28}$$
, ...
b.
$${{1\over2}}$$
, ___, ___,
$$4$$
,
$$8$$
, ___, …
c.
$$5$$
, ___, ___, ___,
$${2{1\over3}}$$
,
$${1{2\over3}}$$
, ...
d.   ___,
$$3$$
,
$${-9}$$
, ___,
$$-81$$
, ___, …
Problem 3
Write a recursive formula for each sequence.
a.
$${11, \space14,\space 17,\space 20,\space 23, …}$$
b.
$${{1\over9},\space {1\over3},\space1,\space 3,\space 9,\space …}$$
c.
$${32,\space 16,\space 8,\space 4,\space 2,\space …}$$


aligns: no