This document discusses sequences and series in mathematics. It begins with an introduction to sequences as ordered lists that follow a pattern or rule. Examples of different types of sequences are given, such as finite vs infinite sequences. Patterns in example sequences are identified. The document then discusses generating patterns in sequences and finding the next terms. Series are introduced as the sum of all terms in a sequence. Examples are given of finding the series of sequences. Students are directed to practice examples in their book and check Canvas for an asynchronous assignment.

1. Welcome
Grade 10-
Grace

2. Can you share to the
class the daily routine
you are doing as you
wake up in the morning

3. How about, can you tell
step by step how do
you your
favorite
me the
process
prepare
food?

4. What do you think
will happen next?

5. What comes
next?
1, 4, 9 16, ...

6. What comes
next?
J, F, M, A, M, J,...

7. What comes
next?
1, 3, 6, 10, 15, ...

8. Sequence and
Series

9. Sequence
A list of numbers or objects
in a special order.
ordered set of
mathematical
quantities called
terms
an arrangement of any objects or a set of numbers
in a particular order followed by some rule

10. Sequence
shows
PATTERNS

11. Spot the
Difference
Sequence A
2, 4, 6, 8, 10, 12, 14, 16
Sequence B
2, 4, 6, 8, 10, 12, 14, 16, ...

12. Types of Sequence
Sequence A is a Finite Sequence becauseit
has a last term
Sequence B is an Infinite Sequence because of the three dots
that signifies no
end

13. Let's Generate Patterns
Example 1:
2, 5, 8, 11, 14
Example 2
7, 9, 11, 13, 15, 17

14. Find the next terms
Example 1:
3n + 1 , 4, 7, 10, ....
6n ,
Example 2
6, 12, 18, 24, ....

15. Let's Apply
You own a fruit stand, To make your display more attractive, you
stack the apples in the shape of a square pyramid with 6 layers,
Starting the top layer, there is only one apple, the second layer
has 4 apples, third
has 9, and so on,
a. write the rule for the number of apples in each layer
b. How many apples are there in the stack?

16. Series
If you add the terms
in the sequence,
the result of the
expression is series

17. Find the series of, ...
Sequence A
2, 4, 6, 8, 10, 12, 14, 16
Sequence B
3, 9, 15, 21, 27, 33

18. Using Summation Notation, we can also
solve sequence
Sequence A
2, 4, 6, 8, 10, 12, 14, 16
Sequence B
3, 9, 15, 21, 27, 33

19. Sequence and
Series
ordered set of
mathematical quantities
called terms
Series is the sum of all
terms in the sequence

20. Let's Get
Involved on
the Task!
Answer
page 11 -
12 on your
book ,
Guided
Practice A -

21. Asynchronous Task
Check your Canvas Course
and Check for the Published
Assignment

22. Thank You for Listening!