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Lesson 10.1, page 926
Sequences and Summation
Notation
Objective: To find terms of
sequences given the nth term and
find and evaluate a series.
DEFINITIONS
sequence – a function in the form of a
list, whose domain is the set of natural
numbers
 term – each number in a sequence
 nth term – general term

Fibonacci Sequence
The Fibonacci Sequence is an infinite
sequence that begins as follows: 1,1, 2,
3, 5, 8, 13, 21, 34, 55, 89, 144, 233,….
 The first two terms are 1. After that, do
you notice a pattern?
 Each term is the sum of the two
preceding terms.

Sequence Notation
Instead of f(x), we write an.
 an= f(n) where n is a natural number
 an is the “nth term”
Types of Sequences
Finite Sequence – has an end
Domain is the set {1, 2, 3,4,…n} n}
Infinite Sequence – does not end
Domain is all natural numbers
What is a sequence? (re-cap)

An infinite sequence is a function whose domain
is the set of positive integers. The function
values, terms, of the sequences are represented
by a1 , a2 , a3 ,...an ...

Sequences whose domains are the first n
integers, not ALL positive integers, are finite
sequences.
Find the 1st 3 terms of the sequence:
n 1
an 
n!
a) 4, 5/2, 6
 b) 0, 3/2, 2/3
 c) 1, 2, 3
 d) 2, 3/2, 2/3

See Example 1, page 927.

Check Point 1: Write the first four terms of
the sequence whose nth term, or general
term is given.
(1)n
a) an  2n  5
b) an  n
2 1
Summation Notation
Ending term
n
Sigma
a
k
 a1  a 2  . . .  an
k=1
Formula to find kth term
Starting term
Summation Notation

The sum of the first n terms, as i goes from 1 to n
n
is given as:
a a  a  a  ...  a  a

i 1

Example:
i
1
2
3
n 1
n
8
 5i  2  [(5  4)  2]  [(5  5)  2]
i 4
 [(5  6)  2]  [(5  7)  2]  [(5  8)  2]
 18  23  28  33  38  102
See Example 5, page 931.

Check Point 5: Expand and evaluate the
sum:
6
a )  2i2
i 1
5
b)  (2k  3)
k 3
5
c)  4
i 1