The document defines sequences and series. It explains that a sequence is an ordered list of numbers with a specific pattern, while a series is the sum of the terms in a sequence. The document provides examples of arithmetic and geometric sequences, and explains how to determine the nth term of each using formulas involving the first term, common difference or ratio, and position of the term. It also discusses finite vs infinite sequences and gives examples of sequences in real world contexts like running training and loan interest.

3. & Series
 Sequence
 An ordered list of
numbers
 A progression of
numbers
 Can be arithmetic,
geometric or neither
 Can be finite or
infinite
 Series
 A value you get when
you add up the terms
of a sequences
 Sum of numbers in a
sequence
 Uses summation
notation Σ (sigma)

4. Find the 10th term of this sequence
2, 5, 8,…
 Start by determining the pattern
 Adding 3 to the previous number
Known as a common difference
 Continue the pattern to get the 10th term
 2, 5, 8, 11, 14, 17, 20, 23, 26,…
 So, the 10thterm is 29

5. Write the first 7 terms of an = 4n + 9
a1 = 13
a2 = 17
a3 = 21
a4 = 25
a5 = 29
a6 = 33
a7 = 37

6. Example:
Determine a rule for the nth term of the
sequence: 1, 16, 81, 256,. . .
 When determining a rule for a sequence you need to compare the
term number to the actual term.
 For this sequence 81 is the 3rd term, so you need to determine how to get 81
from 3.
Rule: an = 4^n

7. Watch the following video on Arithmetic
and Geometric Sequences
http://www.virtualnerd.com/algebra-2/seque

8. 1. 3, 8, 13, 18, 23,…
2. 1, 2, 4, 8, 16,…
3. 24, 12, 6, 3, 3/2,
3/4,…
4. 55, 51, 47, 43, 39,
35,…
5. 2, 5, 10, 17,…
6. 1, 4, 9, 16, 25, 36,
…
Answers:
1. Arithmetic, the common
difference is 5.
2. Geometric, the
common ratio is 2.
3. Geometric, the
common ratio is ½.
4. Arithmetic, the common
difference is -4.
5. Neither, no common
ratio or difference.
6. Neither, no common
ratio or difference.

9.  Infinite
 A sequence that goes
on forever
Example:
14, 28, 42, 56, 70,…
 Finite
 A sequence that has
an end
Example:
1, 3, 9, 27, and 81.

10.   Geometric
  Common Ratio
 Examples:
 2, 4, 8, 16, 32, 64,…
 3, 9, 27, 81, 243,…
 ½, ¼, 1/8, 1/16, 1/32,…
  Arithmetic
  Common Difference
 Examples:
 1, 2, 3, 4, 5,…
 1, 11, 21, 31, 41,…
 3, 0, -3, -6, -9,…

11. an = a1 + (n - 1)d
a1 is the first term in the sequence
n is the number of the term you are
trying to determine
d is the common difference
an is the value of the term that are
looking for

12. Use the arithmetic formula to determine the 100thterm of
the following sequence:
75, 25, -25, -75, -125,…



a1 = 75
n = 100
d = -50
an = a1 + (n - 1)d
= 75 + (100 – 1)(-50)
= -4875

13. Suppose you are training to run a 6 mile
race. You plan to start your training by
running 2 miles a week, and then you
plan to add a ½ mile more every week.
At what week will you be running 6
miles?

14. 


The first term of the sequence will be the initial number
of miles you plan on running.
The common difference of the sequence will be the ½
mile that you increase every week.
n will stand for the number of weeks it will take you to
reach 6 miles.
an = a1 + (n - 1)d
6 = 2 + (n – 1)(1/2)

15. an = a1*r(n--1)



a1 is the 1st term of the sequence
an is the value of the term that are
looking for
n is the number of the term you are

trying to determine
r is the common ratio between terms

16.  Use the geometric rule to determine the 10thterm
of this sequence:
 4, 20, 100, 500



a1 = 4
n = 10
r = 20/4 = 5
an = a1*r(n-1)
= 4 * 5(10-1)
=7812500

17. Example of a Geometric
Sequence in the Real
World
Suppose you borrow $10,000
from a bank that charges 5%
interest. You want to determine
how much you will owe the bank
over a period of 5 years.

18. The first term in the sequences will be
the initial amount of money borrowed,
which is $10,000.
The common ratio is 105%, this can be
represented as 1.05 as a decimal.
n is the number of years you have the
loan.
an = $10,000(1.05)((5--1)

19. Thank you