Download 13.1 Finite Sequences

Warm -up
• Suppose angle A is acute and cos A 
5
. Find sin2A and cos 2A.
13
SEQUENCES AND
SERIES
Chapter 13
•
•
Identify arithmetic or geometric sequence.
Find a formula for a sequence nth term.
What is a sequence?
Set of numbers (called terms) that are arranged in a
particular order.
The
set of positive odd integers
The set of positive multiples of 3
What is a series?
A series is an indicated sum of
the terms of a sequence of
numbers.
The
sum of the cubes of the first
twenty positive integers.
The sum of the first 100 positive odd
integers
There are two special
types of sequences:
Arithmetic – constant difference
The difference between any two consecutive terms is
equal-----Constant Difference
Geometric – constant ratio
The ratio of any two consecutive terms is constant---Constant Ratio
Arithmetic or Geometric?
18, 24,30,36,...
5,10, 20, 40,...
1  2, 2  3,3  4, 4  5,...
3
3
3
3
5, 10, 20, 40,...
15,11, 7,3,...
64, 32,16, 8, 4,...
Is there a
common
difference or a
common ratio?
EXAMPLE OF NOTATION
• t1 – First term
• t2 – Second term
• tn – nth term
tn  5n  2
t1  7
t2  12
Arithmetic Sequence Formula
tn  t1  (n  1)d
Geometric Sequence Formula
tn  t1  r
n 1
Identify the sequence as arithmetic,
geometric or neither. Find the nth
term.
36, 12, 4,...
A sequence of numbers is defined as
the positive multiples of 3. What is
the 105th term?
Graphing
Find the formula for the nth term and
then sketch the graph of the sequence.
• 3, 5, 7, ….
• The graph of this
sequence only
represents discrete
points…specific set.
Graphing
Find the formula for the nth term and
then sketch the graph of the sequence.
• 3, 4.5, 6.75, ….
• The graph of this
sequence only
represents discrete
points…specific set.
Homework
• P. 476 1-25 odd.
Warm-up
• Find the exact value of
formula.
cos75
using a sum/difference
Arithmetic and
Geometric
Sequences Day 2
Finding a sequence given 2 terms.
Finding a term
• In a geometric sequence, t3=12 and
t6=96. Find t11
In a sequence, the second term is 2 and
the 5th term is 16. Find the tenth term
if the sequence is
a) arithmetic
b) geometric
Find the number of multiples of 6
between 28 and 280.
How many 4 digit numbers are not
divisible by 11?
Given the sequence:
3
4, x, x
2
a) Find x if the sequence is
Arithmetic
Geometric
Homework
• Day 2 13.1 P. 477 29-41 odd
• Day 3 13.1 P. 477 47, 49, 50