Download 9.1 Series and Sequences

9.1 Series and Sequences
Understand NOTATIONToday is a language of asking you to
find terms in patterns
List the next three numbers
4, 10, 16, 22…
1, 4, 9, 16, …
1, 1, 2, 3, 5, 8, 13…
Vocabulary
• Sequence- A list of numbers that may or may not be in a
pattern; a function whose domain is a set of positive integers
(whole numbers)
• Term- a number in the sequence
NOTATION:
an is an identified sequence
n stands for the term number/position
Example an= 3n -2
Example a1 = 3(1)-2 = 1
Example a2 = 3(2)-2 = 4 …
Thus an= 1, 4, 7, 10,…
Examples
Page 621 # 3
an = 2n
Find the first five terms of the sequence
(Meditate and let notation sink in)
Vocabulary
• Infinite sequence- The set of all terms in a
sequence; Goes on forever with no end
a1 , a2 , a3 , …, an , …
• Finite sequence- If the set includes only up to
a set/fixed/finite nth term; Ends
a4 , a5 , a6 , …, an
Recursive Sequence
• Recursive Sequence- A sequence in which
previous term(s) are NEEDED to find the next
Example of finding a recursive
sequence #55
a1 =28
ak+1 =ak - 4
Write the recursive sequence/function
for Fibonacci Sequence
1,1,2,3,5,8, …
Factorials!!!
• Notated by n! (read n factorial)
• The factorial of a non-negative integer n is the
product of all positive integers (whole
numbers) less than and equal to n.
5!= 5•4•3•2•1 = 120
Find ! on your calculator!!!
Evaluating Factorials
Coming up with shortcuts
• #63 4!/6!
• #68 (n+2)!/n!
Homework:
• 9.1Page 621
• #s 2-5; 7-13(odd); 25-27; 31; 55-57; try
59&60; 63-69