lecture notes

1. Illustrating
Arithmetic
Sequence

2. Arithmetic Sequence
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
AguinaldoHighway, 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.

3. Arithmetic Sequence
Which of the following sequences is an arithmetic sequence?
Why?
1. 3, 7, 11, 15, 19
2. 4, 16, 64, 256
3. 1, 4, 9, 16, 25, 36
4. 1, 0, -1, -2, -3
5. 9.5, 7.5, 5.5, 3.5, …

4. Answer the following problem.
A merchandiser in Alfa Mart was tasked
to stack 22 cans of Evaporated milk with
10 cans at the bottom of the stack.
Arithmetic Sequence

5. Arithmetic Sequence

6. Arithmetic Sequence
1. Write the number of cans per layer on the
space provided below.
__, __, __, __, __, __, __, __, __, __
2. Does the number of cans in each layer of
the stack show an arithmetic sequence?
Explain your answer.
3. If it shows an arithmetic sequence, then
what is the common difference?

7. - a sequence where every term after the first
is obtained by adding a constant
- 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 terms in the arithmetic
sequence.
Arithmetic Sequence

8. Emer is a runner from Naic. He plans to join an ultra-
marathon of 50 km from Naic town plaza to the
Kaybiang tunnel next month. During the first day of his
training he ran 5 km from Naic town plaza to barangay
Muzon. To improve his stamina and endurance, he
increased the distance he runs by 1.5 km every day.
What is the distance that he will run on the 7th
day of his
training?
Arithmetic Sequence

9. What is the 10th
term of the arithmetic sequence
5, 12, 19, 26, …?
Arithmetic Sequence

10. What is the 21st
term of the arithmetic sequence
7, 13, 19, 25, …?
Arithmetic Sequence

11. What is the 21st
term of the arithmetic sequence
7, 13, 19, 25, …?
Arithmetic Sequence

12. Find of the sequence 4,7,10,13,16, …
Arithmetic Sequence

13. Find 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 = ½; n = 16
4. –10, –6, –2, 2, 6, … n = 27
5. 3, , 2, ,1,… n = 28
Arithmetic Sequence

14. 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?
Arithmetic Sequence

15. 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?
Arithmetic Sequence

16. 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 10years?
Arithmetic Sequence

17. Find the nth term of each arithmetic sequence.
1. , ,
2. , ,
3. , ,
4. , ,
5. , ,
Arithmetic Sequence