The document defines sequences as sets of numbers governed by a rule or pattern. Finite sequences have a limited number of terms with a known last term, while infinite sequences have countless terms continuing without end. Examples are provided of finite and infinite sequences. The document explains how to determine the next term in a sequence given prior terms, and asks readers to list the first five terms of sample sequences and identify them as finite or infinite.

1. Complete the following:

2. OBJECTIVES
Define sequence, finite and infinite
sequence.
List the next few terms given several
consecutive terms of a sequence.
Appreciate the concept of generating
patterns.

3. SEQUENCE
is a set of numbers that are governed by a
certain rule or that follow a certain pattern.
is a functions whose domain is the set of
positive integers or a finite subset of
positive integers.

4. SEQUENCE
Each number in the list is called a term.
EXAMPLES:
Sequence 1 Sequence 2
2,4,6,8,10 2,4,6,8,10,…
Term 1, 2, 3, 4, 5 Term 1, 2, 3, 4, 5
Domain – relative position of each term (1,2,3,4,5) Usually
begins with position 1 unless otherwise stated.
Range – the actual “terms” of the sequence (2,4,6,8,10)

5. SEQUENCE CAN BE FINITE OR INFINITE
FINITE INFINITE
1, 3, 5, 7 6,12, 18, 24, …
20, 40, 60, 80 7, 14, 21, 28, …
5, 10, 15, …, 60 1, 8, 27, 64, 125, …

6. SEQUENCE CAN BE FINITE OR INFINITE
Finite Sequence is a sequence that contains
a limited number of terms. It means that
the last term of the sequence is known.
Example:
2, 4, 6, 8, 10 and 3, 6, 9, 12, 15, 18

7. SEQUENCE CAN BE FINITE OR INFINITE
Infinite Sequence is a sequence that contains a
countless number of terms. The number of the
term in sequence continues or it has no end.
The ellipsis (…) to the end of the sequence
shows that the sequence is infinite.
Example:
1, 3, 5, 7, 9, … and 1, 2, 3, 5, 6, 7, …

8. EXAMPLE
Determine how the next term in each
sequence can be found. Then find the next
term in the sequence.
1. 7, 14, 21, 28, ___
2. 1, 3, 9, 27, ___
3. 5, -6, -17, -28, ___
4. 𝟐,
𝟏
𝟐
,
𝟏
𝟖
,
𝟏
𝟑𝟐
, ___

9. Boards Up!
Write at least the first 5 terms of the following sequence, then
tell whether the sequence is finite or infinite sequence.
1. Counting number from 1 – 20.
2. Multiples of 3.
3. Even numbers from 4 – 100.
4. Odd numbers.
5. Prime numbers from 2.

10. Examples:
1. The table below shows the cost of renting the Cavite
Hall at Island Cove Resort and Leisure Park in Kawit, Cavite
depending on the number of attendees.
Number of
Persons
Rental Cost in
Peso
20 6200
25 6500
30 6800
35 7100

11. SEATWORK 1:
1. It is an ordered of numbers that
follows a pattern or rule.
a. Sequence
b. Series
c. Algebra
d. Geometry

12. SEATWORK 1:
2. What are the next 3 terms of the
sequence 2, 4, 6, __, __, __.
a. 1, 2, 3
b. 8, 10, 12
c. 3, 4, 5
d. 3, 5, 7

13. SEATWORK 1:
3. Which of the following sequence
illustrates an infinite sequence.
a. 1, 2, 3, 4, 5, … 10
b. 2, 4, 6, 8, 10
c. 3, 6, 9, 12, 15, ….
d. 5, 10, 15, 20, 25

14. SEATWORK 1:
4. The sequence 1/3, 1/6, 1/9, 1/12,
1/15 is an example of a finite sequence.
a. True
b. False
c. Maybe
d. I don’t know

15. SEATWORK 1:
5. It is a symbol that tells you that the
sequence is infinite.
a. Greater than
b. Less than
c. Equal
d. Ellipsis