This presentation provides a drill on addition or subtraction of monomials as a practice on the beginning of the slides. It also presents the definition of sequence, arithmetic and geometric sequence with their examples and an activity to perform.

2. QUARTER 1
WEEK 3

3. DRILL

4. (-6a) – (4a)

5. (5n) + (-16n)

6. (7k) - (18k)

7. (-4b) - (-12b)

8. (12y) + (-12y)

9. SEQUENCE
- is a set of
numbers written
in specific order.

10. a. 4, 8, 16 32, 64, 128, …
b. 3, 15, 75, 375, …
c. 6, 12, 18, 24, …
d.
1
3
,
1
6
,
1
12
,
1
24
, …
c. 6, 12, 18, 24, …

11. GEOMETRIC
SEQUENCE

12. 4, 8, 16, 32, 64, 128,…
x 2 x 2 x 2 x 2 x 2
rule: multiplying by 2
a1 a2 a3 a4 a5 a6

13. 3, 15, 75, 375, 1875,…
x 5 x 5 x 5
rule:Multiplying by 5
x 5

14. a. 3, 9, 27, 81, ___ , __
b. 48, 24, 12, 6, __ , __
243 729
3
2
3
Identify the next two terms of the sequence.
x3 x3
÷2 ÷2
x3
÷2

15. When is a given
sequence
arithmetic or
geometric?

16. Arithmetic Sequence
is a sequence where every
term after the first term is
obtained by adding a
constant called the
common difference.

17. Geometric Sequence
(Geometric Progression)
-is a sequence where each
term after the first term is
obtained by multiplying
the preceding term by a
nonzero constant called
the common ratio.

18. 10, 20, 30, 40, 50
ARITHMETIC SEQUENCE
GEOMETRIC SEQUENCE
2, 4, 8, 16, 32, …
+10 +10 d
x2
+10
x2 x2 r
common difference
common ratio

19. How do we find the common
difference of an arithmetic
sequence?
d = a2 – a1
d = a3 – a2

20. How do we find the
common ratio of a
geometric sequence ?

21. Example 1:
2, 4, 8, 16 32, 64, …
r =
𝑎2
𝑎1
r = = 2
4
2
=
𝑎3
𝑎2
=
𝑎4
𝑎3

22. Example 1:
2, 4, 8, 16 32, 64, …
4
2
=2
8
4
=2
16
8
=2
32
16
= 2
64
32
= 2
common ratio (r) = 2

23. Example 2:
r =
𝑎2
𝑎1
=
𝑎3
𝑎2
=
𝑎4
𝑎3
r =
15
3
=
75
15
=
375
75
= 5
3, 15, 75, 375, …

24. Example 3:
r =
𝑎2
𝑎1
=
𝑎3
𝑎2
=
𝑎4
𝑎3
r =
−12
6
=
24
−12
=
−48
24
= -2
6, -12, 24, -48, …

25. Example 4:
r =
𝑎2
𝑎1
=
1
4
1
2
=
1
4
●
2
1
r =
𝑎3
𝑎2
1
2
,
1
4
,
1
8
,
1
16
, …
=
1
8
1
4
=
1
8
●
4
1
=
4
8
=
1
2
=
2
4
=
1
2
1
2
1
2

26. Geometric Sequence
(Geometric Progression)
x ÷
Arithmetic Sequence
(Arithmetic Progression)
+ −

27. YOUR TURN

28. Identify if it is arithmetic or
geometric. If it is geometric,
identify the common ratio.
a. 6, 13, 20, 27, 34,…
arithmetic

29. Identify if it is arithmetic or
geometric. If it is geometric,
identify the common ratio.
b. 9, -9, 9, -9, 9,…
geometric; r = -1

30. Identify if it is arithmetic or
geometric. If it is geometric,
identify the common ratio.
c. 27, 9, 3, 1,
1
3
,…
geometric; r =
1
3

31. Identify if it is arithmetic or
geometric. If it is geometric,
identify the common ratio.
d.
1
2
, 1,
3
2
, 2,
5
2
, 3, …
arithmetic

32. Identify if it is arithmetic or
geometric. If it is geometric,
identify the common ratio.
e. 0.2, 0.4, 0.8, 0.16,…
geometric; r = 2