The document discusses arithmetic sequences and provides examples and explanations. It defines an arithmetic sequence as a sequence where each term is obtained by adding a constant to the preceding term. It explains that the common difference is this constant value, which can be found by subtracting consecutive terms. The formula for the nth term of an arithmetic sequence is given as an = a1 + (n-1)d, where a1 is the first term, n is the term number, and d is the common difference. Several examples are worked out applying this formula to find specific terms of given arithmetic sequences.

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your heartbeat fast
and makes you
crazy.

2. You can drop me
from the tallest
building and I’ll be
fine, but if you drop
me in the water I die.
What am I?
START TIMERTIME’S UP!

3. What gets wetter
and wetter the more
it dries?
START TIMERTIME’S UP!

4. Saulog Transit Inc. is one of the many bus
transportation companies in the Philippines servicing
routes between Cavite and Metro Manila, Olongapo
or Baguio City. One day, on its way back to its terminal
at Mendez, via Aguinaldo Highway, one (1) passenger
went down at SM City Bacoor, then, another four (4)
passengers went down to Robinson’s Place Imus,
seven (7) passengers went down to Robinson’s Place
Pala-pala and ten (10) passengers went down to
Lourdes Church at Tagaytay.

5. Arithmetic
Sequences

6. Illustrative Example 1:
Using the generated sequence from
the previous scenario:

7. The sequence generated from the given
scenario which is 1, 4, 7, 10 is an example of
an Arithmetic Sequence because it is formed
by adding a constant number which is 3 to
the preceding term to obtain the next. The
constant number 3 is the common
difference, denoted as d, which can be
obtained by subtracting two consecutive
terms (𝑑 = 𝑎 𝑛 − 𝑎 𝑛−1) .

8. Find the 10th term of the sequence
3, 8, 13, 18, …
Solution:
Note that 𝑎1 = 3, 𝑑 = 5 and 𝑛 =
10
𝑎 𝑛 = 𝑎1 + 𝑛 – 1 𝑑

9. 𝑎10 = 3 + 10 − 1 5
𝑎10 = 3 + 9 5
𝑎10 = 3 + 45
𝑎10 = 48
That is, 3, 8, 13, 18, 23, 28, 33,
38, 43, 48  10th term

10. Illustrative Example 3:
In the arithmetic sequence 5,
9, 13, 17,… which term is 401?
𝑎 𝑛 = 𝑎1 + 𝑛 − 1 𝑑

11. 1.How is Arithmetic
Sequence formed?

12. 2. How to get the
common difference in
an arithmetic
sequence?

13. 3. How to find the nth
term an arithmetic
sequence?

14. a. Find 𝑎45 of the
sequence 4, 7, 10, 13,
16, …

15. 𝑎 𝑛 = ___ + (___ − 1)___
𝑎 𝑛 = 4 + (____)3
𝑎 𝑛 = 4 + (____)
𝑎 𝑛 = _____

16. b. Which term of the
arithmetic sequence 7,
14, 21, 28, … is 105?

17. ____ = _____ + (𝑛 − 1)____
105 = 7 + ____ − ____
105 = ______
_____ = 𝑛

18. Exercise# 1.4. Directions: Find 𝑎 𝑛 for each
of the following arithmetic sequence.
1. 𝑎1 = 5; 𝑑 = 4 ; 𝑛 = 11
2. 𝑎1 = 14; d = –3 ; n = 25
3. 𝑎1 = 12; 𝑑 =
1
2
; 𝑛 = 16
4. – 10, – 6, – 2, 2, 6, … 𝑛 = 27
5. 3,
5
2
, 2,
3
2
, 1, … 𝑛 = 28

19. START TIMERTIME’S UP!
TIME LIMIT:
10 minutes

20. 1. 44
2. −58
3.
39
2
𝑜𝑟19.5
4. 94
5. −
21
2
𝑜𝑟 − 10.5

21. Collaborative Work
G.1- #1 and 5
G.2- #2 and 4
G.3- #3 and 2
G.4- #4 and 3
G.5- # 5 and 1
START TIMERTIME’S UP!

22. 1. You went to a hiking with your friends at Pico de Loro at Maragondon, Cavite.
Upon reaching the summit, you drop a coin. The coin falls a distance of 4𝑓𝑡 for the
first seconds, 16𝑓𝑡 for the next, 28𝑓𝑡 on the third, and so on. Find the distance the
coin will fall in 6 seconds?
2. Antonio is studying Chabacano, a native dialect from Cavite City and Ternate. He
started practicing one (1) word for an hour and decided to add two more words
every succeeding hour. If the pattern continues, how many Chabacano word did he
learn in one day?
3. Rico bought an e-bike at 𝑃ℎ𝑝29,000. If it depreciates 𝑃ℎ𝑝500 in value each
year, what will be its value at the end of 10 years?
4. Tinapa (smoked fish) is best paired with Atchara (pickled papaya). Diana, a
tinapa vendor in Salinas, Rosario, Cavite, decided to sell atchara at her store. On
the first week, she started to sell 15 atchara bottles and due to high demand, she
decided to add 7 more bottles on each succeeding weeks. Supposed that the
pattern continues, how may week is needed to sell 57 atchara bottles?
5. A Zumba Program calls for 15 minutes dancing each day for a week. Each week

23. 1. You went to a hiking with your friends at Pico de Loro
at Maragondon, Cavite. Upon reaching the summit, you
drop a coin. The coin falls a distance of 4𝑓𝑡 for the first
seconds, 16𝑓𝑡 for the next, 28𝑓𝑡 on the third, and so on.
Find the distance the coin will fall in 6 seconds?
2. Antonio is studying Chabacano, a native dialect from
Cavite City and Ternate. He started practicing one (1)
word for an hour and decided to add two more words
every succeeding hour. If the pattern continues, how
many Chabacano word did he learn in one day?

24. 3. Rico bought an e-bike at 𝑃ℎ𝑝29,000. If it depreciates
𝑃ℎ𝑝500 in value each year, what will be its value at the
end of 10 years?
4. Tinapa (smoked fish) is best paired with Atchara
(pickled papaya). Diana, a tinapa vendor in Salinas,
Rosario, Cavite, decided to sell atchara at her store. On
the first week, she started to sell 15 atchara bottles and
due to high demand, she decided to add 7 more bottles
on each succeeding weeks. Supposed that the pattern
continues, how may week is needed to sell 57 atchara
bottles?

25. 5. A Zumba Program calls for 15 minutes
dancing each day for a week. Each week
thereafter, the amount of time spent dancing
increases by 5 minutes per day. In how many
weeks will a person be dancing 60 minutes each
day?

27. An arithmetic sequence is a
sequence where every term
after the first is obtained by
adding a constant.

28. Common difference (d) is the constant
number added to the preceding term of
the arithmetic sequence. It can be
calculated by subtracting any two
consecutive term in the arithmetic
sequence. The formula for the general
term of an arithmetic sequence is 𝒂 𝒏 =
𝒂 𝟏 + (𝒏 − 𝟏)𝒅