This document provides information about arithmetic sequences including definitions, formulas for finding the sum of terms in an arithmetic sequence, and examples. The objectives are to be able to find the sum of an arithmetic sequence and understand the importance of arithmetic sequences. Key points covered include the definition of an arithmetic sequence as a sequence where the difference between consecutive terms is constant, the formula for finding the sum of terms which involves the first term, last term, number of terms, and common difference, and examples of problems using the formula. Students will do activities working with arithmetic sequence problems.

1. SUM OF
ARITHMETIC SEQUENCE
P r e s e n t e d b y :
W e n n i e R o s e V a l d e z
M o n i c a S . Y a r i z

2. OBJECTIVES
At the end of this lesson, the student should be
able to:
1. find the sum of the sum of the given arithmetic
sequence; and
2. appreciate the importance of sum of arithmetic
sequence to our daily life.

3. ARITHMETIC SEQUENCE
- is a sequence of numbers such that the
difference from any succeeding term to its
preceding term remains constant
throughout the sequence. The constant
difference is called common difference of
that arithmetic progression.

4. What would be the next?
5, 10, 15, 20, 25, 30

5. What would be the next?
15, 30, 45, 60, 75

6. What would be the next?
1, 3, 9, 27, 81, 243

7. 1. How did you find the
next number?
2. what have you notice
with the given set of
numbers?

8. 5, 10, 15, 20, 25 30
+
5
+
5
+
5
+
5
+
5
NUMBER PATTERN - ordered list of
numbers whis is also called
sequence.
TERM - each number in the
sequence.

9. Sum of Arithmetic
Sequence
Formula:
1.
2.
𝑆𝑛 =
𝑛
2
2𝑎1 + (𝑛 − 1)𝑑
𝑆𝑛 =
𝑛
2
𝑎1 + 𝑎𝑛

10. EXAMPLE PROBLEMS:
1. Find the sum of the 25 terms of an arithmetic
sequence 3, 7, 11, 15,..
2. The sum of the first 10 terms of an arithmetic
sequence is 530. What is the first term if the
last term is 80?
3. The third term of an arithmetic sequence is -5
and the sixth term is 7. What is the sum of
the first 10 terms?

11. ACTIVITY
RULES:
Teacher will draw out names on basket 1.
The names of students will be called
simultaneously after the draw and student will
draw out on basket 2, once, for questions and
each draw corresponds an item for them to
work with it.
After solving it, they will present it.
A student will present his/her answer in front
of the class.

12. ASSIGNMENTS
I. List Down, how can we use arithmetic sequence in our
daily life?
II. Answer the following question (Show your Solution).
1.Find the 7th term of the arithmetic progression: 18, 23,
28, ...?
2.What is the common difference of the arithmetic
progression: 5, 2, -1, -4, . . . ?
3.What is the sum of first four terms of the arithmetic
sequence {2, 4, 6, 8, 10}?

13. Thank you
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