ppt

1. Here starts
the lesson!
Grade 10
Sunstone

2. At the end of the lesson, the students are expected to:
1. @ Illustrates an arithmetic sequence;
2. @ Determines arithmetic means, nth term
of an arithmetic sequence and sum of the
terms of a given arithmetic sequence
Objective

3. Prayer
Our most precious
Heavenly Father, We thank
you for the opportunity to
begin this new lesson. We
ask that you Bless the
students and the teacher
that make our school a great
place. We pray that you will
guide us in all ways, so
that we will seek your Will
in everything that we do. We
ask this in the name our
Lord Jesus, our Lord. Amen
Checking of

4. 01
REVIEW
Who remembers what is an
sequence? An arithmetic
sequence?

5. -is a function whose
domain is the finite
set {1,2,3,…,n} or the
infinite set {1,2,3,…}
Sequence
- Is an arrangement of
objects, numbers or even
figures, patterns which
follows a certain patterns.
Sequence

6. ● Example:
1, 2, 3, 4, 5
● 1st term is “1”,
and last term is
“5”
● 2, 4, 6,…20
1st term is “2”,
and last term is 20
Finite Sequence Infinite Sequence
- If it has a 1st term and last
term.
- If it has a 1st term but NO last
term.
● Example:
5, 10, 15, 20, …
● 1st term is “5”,
and NO Last term
● 7, 9, 11, 13, …
1st term is “7”,
and NO Last term

7. Observe the following sequences. What is the
pattern you observed in each sequence?
ACTIVITY: Identifying Patterns
1. 4, 7, 10, 13, …
2. 33, 38 , 43, 48, …
3. -2, -6 , -10, -14, …
4. 100, 98, 96, 94, …
5.
1
2
, 1, 1
1
2
, 2, …
Adding 3
Adding 5
Subtracting 4 Adding -4
Subtracting 2 Adding -2
Adding
1
2
+3
+5
+3 +3
+5 +5
±4 ±4 ±4
±2 ±2 ±2
1/2 1/2 1/2

8. -it is sequence where
every term after the
first term is obtained
by adding a constant
called the common
difference (d).
Arithmetic Sequence
To find the common
difference(d), you
can simply
subtract any term
by its preceeding
term.
Arithmetic Sequence

9. Arithmetic Sequence is a sequence where every
term after the first is obtained by adding a
constant called common difference.
The sequences 1, 4, 7, 10, … and 15, 11, 7, 3, …
are examples of arithmetic sequence since each one
has a common difference of 3 and -4, respectively.

10. 1. Determine if the sequence is arithmetic or not. If it is, find
the common difference and the next three terms of the sequence.
-4, 3, 10, 17, …
Solution: To find out if the sequence is arithmetic, there must
be a common difference between any two consecutive terms in the
sequence.
-4, 3, 10, 17, …
Since the common difference is 7, the next three terms are
obtained by adding 7 to the preceding term.
-4, 3, 10, 17, 24, 31, 38
Thus the common difference is 7 and the next three
terms are 24, 31, 38.
3 – (-4) 10 – (3) 17 – (10)
=7 =7 =7
Because there is a COMMON
DIFFERENCE between
consecutive terms, the
sequence is arithmetic.

11. Is the meaning of
Arithmetic Sequence
clear to you? Are
you ready to learn
more arithmetic
sequences?
If so, then you
have to prepare a ½
crosswise sheet of
paper.
½ Sir?????
YES

12. 1. 3, 12, 21, __, __, __,
2. 8, 3, -2 __, __
3. 5, 12, __, 26, __
4. 2, __, 20, 29, __
5. __, 4, 10, 16, __
Find the missing terms in
each arithmetic sequence.
6. 17, 14, __, __, 5
7. 4, __, __, 19, 24 …
8. __, __, __, 8, 12, 16
9. -1, __, __, __, 31, 39
10. 13, __, __, __, -11, -17

13. 1. 3, 12, 21, 39, 48, 57
2. 8, 3, -2 __, __
3. 5, 12, 19, 26, 33
4. 2, 11, 20, 29, 38
5. -2, 4, 10, 16, 22
Find the missing terms in
each arithmetic sequence.
6. 17, 14, 11, 8 , 5
7. 4, 9, 14, 19, 24 …
8. -4 , 0 , 4, 8, 12, 16
9. -1, 7, 15, 23, 31, 39
10. 13, 7, 1, -5, -11, -17

14. Given 7p+4, 5p+12, 2p-1 as an
arithmetic sequence, what is p?
What is the common difference?
7p+4, 5p+12, 2p-1
a1 a2 a3
a2 - a1 = a3 - a2
LINEAR Equation

26. General or nth
Term of
Arithmetic
Sequence
What Is This
Topic About?
Arithmetic Sequence can be
expressed as an equation
(rule)
Arithmetic Sequence general
rule is
An = a1 + (n-1)d
First Tern
Common Difference
Number of Terms

27. Example Abstraction
Graph the linear equation
that passes through the given
points (-5,0), (2,-3).
Giving of Examples

29. What is a
Linear
Equation?

30. APPLICATION

31. Evaluation
Graph the linear
equation that
passes through
the given points
(-3,5), (5,-5).
.

32. Assignment
Find the slope
of the line
passing through
(-3,-5) and
(2,1).

33. Thanks!
Do you have any
questions or
clarifications?
Fell free to contact
me at
viczy2011@gmail.com
or 09054604220