1. Lesson 10.1: Sequences & Summation Notation
Algebraic formula first n terms
Factorial notation
Series
Summation or Sigma notation

2. Sequence: an ordered collection of comma-separated terms
, 9, 13, 17, _____
, 1, -1, 1, -1, 1, _____
, 1, 2, 3, 5, 8, 13, 21, ______
, , 100, - 10, 1, ______
a + b, 2b, - a + 3b, - 2a + 4b, _________

3. An infinite sequence { an } is a function whose domain
is the set of positive integers*. The function values
a1, a2, a3, a4, ... an, ...
are the terms of the sequence. If the domain of the
sequence consists of only the first n positive integers,
then the sequence is a finite sequence. [p 656]
Example: infinite sequence
5, 9, 13, 17, , an, . . . an
nth term a1
first term
What is a6? ________
Occasionally, sequences start with n=0

4. Algebraic formula first n terms
Find the first four terms of the indicated sequence.
an = 3n – 2
a1 = 3(1) – 2 =
sequence:
a2 = 3(2) – 2 =
a3 = 3(3) – 2 =
a4 =

5. Find the first four terms of the indicated sequence.

6. Practice: p # 7 & 10
Write the first five terms of the indicated sequence.

7. Algebraic formula first n terms
Write an expression for the apparent nth term of the sequence
, 3, 5, 7, . . .
n: n
terms: an
Answer: an = 2n - 1

8. Write an expression for the apparent nth term of the sequence
Answer:
, 5, 10, 17, . . .
n: n
terms: an
Answer:

9. n: n
terms: an
Answer: an =
Answer: an =

10. Factorial Notation [p 658]
If n is a positive integer, then n factorial is defined by
n! = 1 · 2 · 3 · 4 · 5 · · · (n – 1) · n
Special case: 0! = 1
4! = 1 · 2 · 3 · 4 = 24
10! = 1 · 2 · 3 · 4 · 5 · · ·10 =
3,628,800
On graphing calculators:
On Ti89: MATH Probability !
On Ti84: MATH PRB !

11. Find the first five terms of the sequence whose nth
term is Begin with n = 0.
sequence:

12. Fractions involving factorials can often be simplified.1. 2. 3. 4.

13. Series: the summation of the terms of a sequence
The sum of the first n terms of a sequence is represented by
where i is the index of summation, n is the upper limit of
summation and 1 is the lower limit of summation*. [p 660]
This is often referred to as sigma notation.
The index does not have to i and the lower index of summation does not have to be 1.

14. Properties of Sums 4(1) + 4(2) + 4(3) + 4(4) + 4(5) = 60
c is any constant
(22 + 2) + (32 + 2) + (42 + 2) + (52 + 2) + (62 + 2) = 100

15. Use Sigma Notation to write a sum
Similar to writing on expression for the apparent nth term.
Place in sigma notation, specifying summation boundaries.
n: n
terms: an
an = 3n - 2
– –
n: n
terms: – – –729 an

16. Homework:
Sequences: p664 #2, 4, 6, 12, 14, 16, 22, 26, 28, 30, 34
Series: pp 664–665 #38, 40, 42, 46, 48, 52, 55