Building a function library & more on arithmetic sequences.

1. Building a Library of Functions
in the library by flickr user svenwerk

3. Find the next three terms in each sequence of numbers ...
in the library by flickr user svenwerk
4, 7, 10, 13, , ,
3, 6, 12, 24, , ,
32, 16, 8, 4, , ,
1, 1, 2, 3, 5, 8,13, , ,

4. 4, 7, 10, 13, , ,

5. Some Definitions
Sequence: An ordered list of numbers that follow a certain pattern (or
rule).
Arithmetic Sequence: (i) Recursive Definition: An ordered list of
numbers generated by continuously adding a value (the
common difference) to a given first term.
(ii) Implicit Definition: An ordered list of numbers where
each number in the list is generated by the equation of a line.
Common Difference (d): (i) The number that is repeatedly added to
successive terms in an arithmetic sequence.
(ii) From the implicit definition, d is the slope of the linear
equation.

6. To Find The Common Difference
d is the common difference d = tn - t(n - 1)
tn is an arbitrary term in the sequence
t(n - 1) is the term immediately before tn in the sequence
To Find the nth Term In an Arithmetic Sequence
tn is the nth term tn = a + (n - 1)d
a is the first term
n is the quot;rankquot; of the nth term in the sequence
d is the common difference
Example: Find the 51st term (t51) of the sequence 11, 5, -1, -7, ...
Implicitly?
Solution: a = 11 t = 11 + (51 - 1)(-6)
51
d = 5 - 11 t51 = 11 + (50)(-6)
= -6 t51 = 11 - 300
n = 51 t51 = -289