Explains How to Generate patterns

1. patterns
Generating
In Sequences

2. Let’s Start!
1. 1, 3, 5, 7, _, _, _
2. 5, 15, 25, _, _, _
3. A, D, G, J, _, _, _
4. 1, 4, 9, 16, 25, _, _, _
5. 1, 3, 6, 10, _, _, _
Find the next
three terms

3. What Is a
Sequence?
A sequence is a set of objects which is
listed in a specific order, one after
another.

4. What Is a
TERM?
Each member or element
in the sequence.

5. The terms in a sequence can
be written as , ,
𝒂𝟏 𝒂𝟐
, , . . . , , . .. which
𝒂𝟑 𝒂𝟒 𝒂𝒏
means 1 is the first term, 2
𝑎 𝑎
is the second term, 3 is the
𝑎
third term, …, is the nth
𝑎𝑛
term, and so on.

6. What Is a
FINITE
SEQUENCE?
A finite sequence contains
a limited number of
terms. This means it has
an end or last term.

7. EXAMPLES:
a) Days of the week: { ,
𝑆𝑢𝑛𝑑𝑎𝑦
, , . . . ,
𝑀𝑜𝑛𝑑𝑎𝑦 𝑇𝑢𝑒𝑠𝑑𝑎𝑦
}
𝑆𝑎𝑡𝑢𝑟𝑑𝑎𝑦
b) First 10 positive perfect squares:
{1, 4, 9, 16, 25, 36, 49, 64, 81, 100 }

8. What Is aN
INFINITE
SEQUENCE?
an infinite sequence contains
a countless number of terms.
The number of terms of the
sequence continues without
stopping or it has no end
term.

9. EXAMPLES:
a) Counting numbers: {1, 2, 3, 4,
5, . . .}
b) Multiples of 5: {5, 10, 15, 20, 15, . .
.}

10. WHAT IS
GENERAL
TERM?
a formula that expresses any term
in the sequence in terms of its
position (n) in the sequence

11. EXAMPLE:
An = 2n
The general term can be written as: an = 2n.
The general term can be written as: an = 2n.

12. EXAMPLE:
Find the first five terms of the
sequence with the general term an
= 2n
The general term can be written as: an = 2n.
The general term can be written as: an = 2n.

13. EXAMPLE:
Find the first five terms of the
sequence with the general term an
= 2n-1
The general term can be written as: an = 2n.
The general term can be written as: an = 2n.

14. EXAMPLE:
Find the first five terms of the
sequence with the general term an
= 2-3n
The general term can be written as: an = 2n.
The general term can be written as: an = 2n.

15. EXAMPLE:
Find the first five terms of the
sequence with the general term an
= (n-3)^n
The general term can be written as: an = 2n.
The general term can be written as: an = 2n.

16. EXAMPLE:
Find the first five terms of the
sequence with the general term an
= (-1)^n
The general term can be written as: an = 2n.
The general term can be written as: an = 2n.
2n-1

17. ACTIVITY NO.1
Find the first five terms of the
sequence with the general term:
The general term can be written as: an = 2n.
The general term can be written as: an = 2n.
1. an= n+4
2. an= 3n-1
3. an=12-3n
4. an=3^n
5. an=(-2)^n

18. QUIZ No.1
Find the first five terms of the
sequence with the general term:
The general term can be written as: an = 2n.
The general term can be written as: an = 2n.
1. an= 7n-3
2. an= 11-9n
3. an=5n+6
4. an= 5n-3
5. an= 11-
9n
6n+2
n^2+3