Introduction on sequence.

2. Sign in on time
Find some quiet place to study
Listen!
Look at the screen
Raise your hand
Answer when teacher calls your name
Don’t draw on the screen
Don’t talk to your friends
Enjoy!

3. 1. How are patterns formed?
2. Where can we see patterns?
3. How will you complete a shape or a number pattern?
4. What is pattern?

5. 1. How are patterns formed?
2. Where can we see patterns?
3. How will you complete a shape or a number pattern?
4. What is pattern?

6. Generate and describe patterns
Find the next few terms of a
sequence

7. Activity 1: “With Pattern or
Without Pattern?”
Direction: Identify if each picture
below shows a pattern or not. If
there is a pattern, put a check
mark (✓) and identify it, otherwise
put a cross mark (x).

9. • A sequence is a function whose domain is either the set
𝟏, 𝟐, 𝟑, … , 𝒏 where n is a natural number or the set of positive
integers.
• Every element in the sequence is called a term and denoted by
a1, a2, a3, a4, …
• From the definition, a sequence is said to be finite if its domain
is the set {1, 2, 3,…,n} and is said to be infinite if its domain is
the set of positive integers.

10. The first sequence is an example of finite sequence since there is
a last term.
Considering the first sequence 3, 9, 27, 81.
We can clearly identify the terms as follows,
First term denoted by a1 is 3
Second term denoted by a2 is 9
Third term denoted by a3 is 27 and
The fourth term denoted by a4 is 81.
And a4 is also the last term of the sequence.

11. The second example is an infinite sequence since there are 3 dots
or ellipsis at the end which signifies continuity of the terms.

12. Identify the following sequence either finite or infinite.
Complete the table below.
Sequence Classification
1. 5, 10, 15, 20, ….
2. 2.1, 2.8, 3.5, 4.2, …
3. 5, 10, 15, 20, …, 100
4. 1, 2, 3, …
5. 1, ¾, ½, ¼
TIMES UP!!
START TIME

13. Identify the following sequence either finite or infinite. Complete
the table below.
Sequence Classification
1. 5, 10, 15, 20, …. (Infinite)
2. 2.1, 2.8, 3.5, 4.2, … (Infinite)
3. 5, 10, 15, 20, …, 100 (Finite)
4. 1, 2, 3, … (Infinite)
5. 1, ¾, ½, ¼ (Finite)

14. Consider the function
an=2n+1
*This function an is considered as the general term of the
sequence.
Let’s find the first 5 terms of the sequence.
For n=1, a1=2(1)+1=2+1=3
For n=2, a2=2(2)+1=4+1=5
For n=3, a3=2(3)+1=6+1=7
For n=4, a4=2(4)+1=8+1=9
For n=5, a5=2(5)+1=10+1=11
Suppose n=12, then, a12=2(12)+1=24+1=25

15. Direction. Answer the following problems for 5 minutes only.
1. Find the first five terms of the sequence whose general
term is an=3n
2. Find the 15th term of the sequence whose general term is
an=((n+1))/n.
3. Find the 10th term of the 1,5,9,13,… .

16. Solution for problem No. 1.
1. Find the first five terms of the sequence whose
general term is an=3n
Given: an=3n
If n= 1, then If n = 2, then
a1=31 a2=32
=3 =9
If n = 3, then If n = 4, then
a3=33 a4=34
=27 =81

17. Solution for problem No. 1. Continued
1. Find the first five terms of the sequence whose
general term is an=3n
If n = 5, then
a5=35
=243
Therefore, the first five terms of the sequence is 3, 9, 27,
81, 243

18. Solution for problem No. 2.
2. Find the 15th term of the sequence whose general
term is an=((n+1))/n.
Given: an=((n+1))/n
If n = 15, then
a15 = ((15+1))/15
a15 = 16/15

19. Solution for problem No. 3.
3. Find the 10th term of the sequence 1,5,9,13,… .
The first 4 terms of the sequence are given, and no general term
provided. So, we need to determine the pattern to generate the
next terms.
Notice that a constant number 4 is added to the preceding term to
get the next term. So, if this pattern continues, then the 10th term
is 37.

20. A. Write F if the sequence is finite or I if the sequence is
infinite.
1. 2, 6, 18, 54
2. 3, 9, 27, 81, …., 729, …
3. -2, 4, -8, 16, …..
4. 100, 97, 94, 91, …, -2
5.1/4,1/8, 1/16, 1/32, 1/64
6. 2, 3, 4, 5, ….., 10
7. 7, 10, 13, 16, 19, 22, 25
8. 4, 9, 14, 19, …
9. 1, 4, 9, 16, 25, …., 144
10. ¼, 2/9, 3/16, 4/25

21. Direction: Answer the given problems in a 1 whole sheet of paper
then upload the JPEG file of your answer to the given link below.
https://forms.gle/2VP5JPYtheCCXd286

22. Direction: Students will answer the reflection in the given link
below using the Google Form.
Let Us Reflect!
1.Why is generating pattern important in problem
solving?
https://forms.gle/z6ckJbTQbscTWEBT6