The document presents a series of exercises focused on sequences, particularly arithmetic sequences, encouraging brain stimulation through problem-solving. It includes various patterns for participants to identify and analyze, such as finding common differences and determining terms in sequences. Additionally, it incorporates activities involving matchsticks to explore mathematical concepts visually and contextually.

1. Let’s Stimulate Our Brain!

2. J M M A O ___
Answer: D – December (months w/ 31
days)

3. T Q P H H O N ___
Answer: D - Decagon

4. 1, 4, 9, 25, ___
Answer: 36

5. 2, 4, 5, 7, 9, 11, ___
Answer: 13 – Local TV Channels

6. R O Y G B I ___
Answer: V

7. 1, 3, 5, 7, 9, 11, 13, 15, ___
Answer: 17

8. 1, 9, 25, 49, 81, ___
Answer: 121

9. A B C E F G ___
Answer: I

10. P E M D A ___
Answer: S

11. 2, 7, 12, 17, 22, ___
Answer: 27

12. 2, 3, 5, 6, 8, 9, ___
Answer: 11

13. 2, 3, 5, 6, 8, 9, ___
Answer: 11

14. A J S ___
Answer: N – November (30 days)

15. M T W T F S ___
Answer: S - Sunday

16. ____
Answer:

17. aabc, aabc, aabc, a_
Answer: a

18. Arithmetic Sequence

19. “What comes after me?”
Find the pattern and continue the
sequences.
1. 5, 8, 11, 14, 17, ___, ___, ___
2. 25, 21, 17, 13, 9, ___, ___, ___
3. 4, 6, 8, 10, 12, ___, ___, ___
4. 9.5, 7.5, 5.5, 3.5, ___, ___, ___
5. 16, 7, -2, -11, ___, ___, ___

20. Let’s Investigate
1. How do you find the activity?
2. What do you observed in the given
exercises?
3. How did you arrived at your answer?
4. Were you able to find the pattern for each
sequence?
5. What mathematical skills or principles did
you use to recognize the pattern and to
get the next number?

21. Activity:”What Do We Have in
Common?”
As a group, you will be needing matchsticks for
these.
1. Below are squares formed by matchsticks.
2. Count the number of matchsticks in each
figure and record the results in a table.
Number of squares 1 2 3 4 5 6 7 8 9 10
Number of matchsticks

22. Analysis
1. Is there a pattern in the number of
matchsticks? If there is, describe it.
2. How is each term (number of
matchsticks) found?
3. What is the difference between any two
consecutive terms?
4. How was the activity?
5. What new thing did you learn from the
activity?

23. Arithmetic Sequence
Consider the following sequences and
observe how the succession of terms is
obtained.
A. 1, 3, 5, 7, … 3 – 1 = 2
5 – 3 = 2
7 – 5 = 2
The common difference is 2.

24. Arithmetic Sequence
B. -3, -6, -9, -12, … -6 – (-3) = -3
-9 – (-6) = -3
-12 – (-9) = -3
The common difference is -3.
C. 1, 1.5, 2, 2.5, 3, … 1.5 – 1.0 = 0.5
2.0 – 1.5 = 0.5
2.5 – 2.0 = 0.5
The common difference is 0.5.

25. Arithmetic Sequence
D. 15, 25, 35, 45, 55 25 – 15 = 10
35 – 25 = 10
45 – 35 = 10
55 – 45 = 10
The common difference is 10.

26. Arithmetic Sequence
A sequence in which each term is
obtained by adding a constant d to the
preceding term. The constant number d is
called the common difference.

27. Arithmetic Sequence
In symbols, if a is the first term, and d is the common
difference, then the terms of an arithmetic sequence can
be enumerated in the following manner:
a1 = the first term
a2 = a1 + d, the second term
a3 = (a1 + d) + d or a1 + 2d
a4 = (a1 + 2d) + d or a1 + 3d
a5 = (a1 + 3d) + d or a1 + 4d
a6 = (a1 + 4d) + d or a1 + 5d
a7 = (a1 + 5d) + d or a1 + 6d
This shows that the coefficient of d is one less than the
number of terms. In general, an = a1 + (n – 1)d.

28. Examples
• Determine the 10th term in the sequence 4, 6, 8,
10, ...
• The second term of an arithmetic sequence is 24
and the fifth term is 3. Find the first term and the
common difference.
• Give the arithmetic sequence of 5 terms if the
first term is 8 and the last term is 100.
• How many terms are there in an arithmetic
sequence with a common difference of 4 and
with the first and last terms 3 and 59,
respectively?

29. Examples
1. Determine whether the sequence is
arithmetic. If it is, give the common
difference.
a. -3, 2, 7, 12, … b. 4, 8, 16, 32, …

30. Application
Answer Learning Task 2 A and B on p. 10

31. Assessment
A. Determine if the given sequence is
Arithmetic or Not.
1. 3, 7, 11, 15, 19
2. 4, 16, 64, 256
3. 48, 24, 12, 6, 3,…
4. 1, 4, 9, 16, 25, 36
5. 1, ½, 0, -½

32. Assessment
B. Use the formula for the arithmetic
sequence to answer the following questions.
1.Find the 25th term of the arithmetic
sequence 3, 7, 11, 15, 19, …
2.Find a1 if a8 = 54 and a9 = 60.
3.Which term of the arithmetic sequence is -
18, given that a1 = 7 and a2=2?

33. Assignment
Answer the following:
1.How many terms are in the arithmetic
sequence whose first term is -3, common
difference is 2, and the last term is 23?
2.What must be the value of k so that 5k – 3,
k + 2, and 3k – 11 will form an arithmetic
sequence?