The document provides an overview of arithmetic sequences, including how to find the common difference and the nth term. It illustrates the concepts with examples and emphasizes problem-solving in arithmetic sequences. Additionally, it discusses practical applications of the arithmetic sequence in real-life scenarios.

1. ARITHMETIC
SEQUENCE
MARK O. AGUSTIN, LPT

2. LEARNING COMPETENCIES
• Find the common difference and the nth
term of an arithmetic sequence.
• Solve problems involving arithmetic
sequence
LEARNING OBJECTIVES
• Illustrate an arithmetic sequence
• Determine the nth terms of an arithmetic
sequence.
• Solve problems involving sequences.

3. ESSENTIAL QUESTION
•How do you compute for
the common difference of
an arithmetic sequence?
•How do you find the nth
term of an arithmetic
sequence?

4. ARITHMETIC SEQUENCE
•Also known as arithmetic
progression
•A sequence where each term
after the first is obtained by adding
a constant (called the common
difference) to the preceding term.
Ex. 4, 8, 12, 16
-5, -2, 1, 4

5. TERM
•Each value in a
sequence
Ex. 4, 8, 12, 16
the 1st
term is 4, 2nd
term is 8, 3rd
term is 12, 4th
term is 16 and so on.

6. GENERAL TERM OF A
SEQUENCE
Where:
= nth term
= 1st
term
=number of terms
= common difference

7. ILLUSTRATIVE EXAMPLE
Find the 20th
term in the
sequence 6, 13, 20, 27, …
Solution:
1. Find the common
difference
d=

8. ILLUSTRATIVE EXAMPLE
Find the 20th
term in the
sequence 6, 13, 20, 27, …
Therefore, the 20th
term is 139.

9. ILLUSTRATIVE EXAMPLE
2. List all given

10. ILLUSTRATIVE EXAMPLE
Find the 30th
term in the
sequence if the 5th
term is -
10 and the common
difference is 6.
Given:
5th
term= -10
d= 6

11. ILLUSTRATIVE EXAMPLE
Find the 30th
term in the sequence if
the 5th
term is -10 and the common
difference is 6.
Solution:
First find

12. ILLUSTRATIVE EXAMPLE
Find the 30th
term in the sequence if the 5th
term is -10 and the common difference is 6.
Solution:
find
Therefore, the 30th
term is 140.

13. ILLUSTRATIVE EXAMPLE
In the arithmetic
sequence, the 4th
term is 30 and the
10th
term is 66. find
the 8th
term.

14. ILLUSTRATIVE EXAMPLE
Given the arithmetic
sequence , find the
10th
term

15. ILLUSTRATIVE EXAMPLE
In an arithmetic
sequence, the 5th
term is 24 and the 11th
term is 60. what is the
common difference.

16. ILLUSTRATIVE EXAMPLE
The 4th
term of an
arithmetic sequence
is -1 and the 6th
term is
9. write the first eight
terms of the
sequence.

17. ILLUSTRATIVE EXAMPLE
Reymund decided to join a gym’s
weight loss program. One week after
joining, he starts losing a constant
amount of weight. Five weeks after
joining the gym, he weighs 165 kg.
ten weeks after, he weighs 150 kg.
assuming that the patterns
continues, find his weight before
joining the gym and the amount of
weight he lost per week.