Rpp Barisan Aritmatika Arithmatic Series

1. LESSON PLAN
Education Units: Senior High School
Class / Semester: X/ Odd
Subject : Mathematics
Material : Arithmetic Series
Time Allocation: 2 x 45 Minutes
A. Main Competencies
1. Respect and appreciate their religion lesson.
2. Respect and appreciate the honest behavior, discipline, responsibility,
carring (tolerance, mutual cooperation), polite, confident, in interacting
effectively with the social and natural environment in a range of social and
existence.
3. Understanding knowledge (factual, conceptual, and procedural) based on his
curiosity about science, technology, arts, culture and events related real
phenomena.
4. Trying to process, and in the realm of concrete (using, parse, compose,
modify, and create) and the realm of the abstract (writing, reading, counting,
drawing, and fabricated) according to the learned in schooland other sources
in the same viewpoint/theory.
B. Basic Competencies
1. Show the logical attitude, critical, analytical, consistent and conscientious,
responsible, responsive and never give up to solving the problem.

2. 2. Having a curiosity, confidence, and interest in math and have a sense of trust
in the power and usefulness of mathematics, which are formed by learning
experiences.
3. Having an open attitude, polite, objective, appreciate the opinions and effort
of friends in group interaction and activities of daily live.
4. Applying the property of logarithm to solve the related problems.
C. Achievement Indicator
1. Active involved in learning.
2. Cooperate in group activities.
3. Solving the related problems using the property of arithmetic series.
D. Learning Objectives
1. Students are able to solve related problems arithmetic series.
2. Students are able to use the property of arithmetic series.
E. Learning Materials
Arithmetic Series
Definition:
If the terms in an arithmetic sequence are added up, so an arithmetics series is
obtained. If U1, U2, U3,... is an arithmetic sequence, then U1 +U2+ U3+… is
arithmetic series. The arithmetic series obtained by adding up the first n terms of
an arithmetics series is notated by Sn.
So, Sn = U1 +U2+ U3+…Un
Property:
Sn = U1 +U2+ U3+U4+U5+…Un-1 + Un is the sum of the first n terms of arithmetic
series, Sn =
2
n
[2a + (n-1)b]

3. =
2
n
[a + Un]
=
2
n
[U1+ Un ].
Now, we will expanding the formula Sn =
2
n
[2a + (n-1)b], we obtain:
Sn =
2
n
[2a + (n-1)b]=
2
n
(2a + bn – b) =
2
n
n2 + n
ba
2
2 
F. Learning Method
Discussion, discovery, and demonstration.
G. Learning Activities
ACTIVITIES DESCRIPTION OF ACTIVITIES TIME
Introduction
1. Teacher say hello and ask students presence.
2. Teacher remind the students about the concept
and property of arithmetic sequence that has been
obtained in the past meeting.
3. Students receive information competence,
material, purpose, benefits, and lessons that have
to be implemented.
5 minutes
Core
Observing
5 minutes1. Students in groups observing about the
arithmetic series problems on the work sheet.
Questioning
5 minutes2. Students ask questions about how to solve
arithmetic series problems.
Exploring 5 minutes

4. 3. Students in groups discuss and try to solve
related problems about arithmetic series on the
work sheet.
Associating
5 minutes4. Students applying the consept and property of
arithmetic series to solve problems.
Communicating
5 minutes
5. Students are presenting the result of group
discussion related with applying the property of
arithmetic series to solve problems.
Closing
1. Students and teacher summarizes the lesson about
arithmetic series.
2. Teacher give quiz to students.
3. Teacher give homework to students.
10 minutes
H. Learning Tools and Resources
1. Media : Power Point and Work Sheet
2. Tools : LCD, Notebook, and Whiteboard
3. Learning source : Buku Siswa Matematika SMA/MA Kelas X
Kemdikbud
D. Assessment.
Assessment procedures:
No Aspects of assessed
Technique of
assessment
Time of assessment

5. No Aspects of assessed
Technique of
assessment
Time of assessment
1 Curiosity Observations Main activities
2
Responsibilities
within the group
Observations Main activities
3
Knowledge Portfolio
Outcome
End of meeting
1. Attitude AssessmentInstrument:
STUDENT’S ATTITUDE DEVELOPMENTOBSERVATION
SHEET
Subjects : Mathematics
Class / Semester : X / 1
Academic Year: 2014/2015
Observationtime : Main Activities.
Basic Competence : No. 2.1, 2.2
The attitudes that are developed in the learning process are curiosity and
responsibility in the group.
A. Curiosity Development Indicators
1. Less good if at all do not attempt to try or ask or indifferent (do not
want to know) during the learning process.
2. Good if has showed the effort to try or ask during the learning
process but not steady / consistent.

6. 3. Very good if shows any efforts to try or ask during the learning
process continuously and steady / consistent.
B. Responsibility Development Indicators (In The Group)
1. Less goodif did not take part in the group.
2. Goodif has showed the effort to take part in doing group
discussionbut not steady / consistent.
3. Very goodif has showed the effort to take part in doing group
discussioncontinuously and steady / consistent.
Give the check mark () in the correspondingcolumns based on
observation.
N
o
Name
Curiosity Responsibilities
LG G VG LG G VG
1
2
3
...
32
VG = Very good G = Good LG = Less good
1. Instrument Assessment:
QUIZ

7. Test Description (Time: Max 10 minutes)
Instruction: Solve the following problems!
1) Given that the first 11 terms of an arithmetic series is Sn = 5n2 + 4n.
in what term number has the value of 159?
Rubric Assesment of Knowledge
Answer Score
From Sn = 5n2 + 4n obtained 5
2

b
, so that b=10.
U1 = S1
= 5(1)2+4(1)
= 9.
Therefore, Un = 9 + (n-1) 10
Un = 159, so
159= 9 + (n-1) 10
159= 9 + 10n – 10
160= 10n
16 = n
So, the term whose value of 159 is the 16-th term
7
25
10
55
3
TOTAL SCORE 100
Singaraja, 5 Maret 2015
Constituent

8. I Made Ari Purwadi
NIM. 1213011002
STUDENTS WORK SHEET
Name of School :
Subjects : Mathematics
Class/Semester : X/I
Topic : Logarithm
Work Instructions
a. This work sheet will help you to understand the material.
b. You are expected to fill out the work sheet after following impressions
matter.
c. Along work sheet you will find the following commands:
 Observing : think the information/material provided
 Questioning : ask about the material
 Exploring : answer the question
 Associating : conclude the answer
 Communicating : present the conclusion
d. Do it in 20 minutes.
Materials:
Sn = U1 +U2+ U3+U4+U5+…Un-1 + Un is the sum of the first n terms of arithmetic
series, Sn =
2
n
[2a + (n-1)b]

9. =
2
n
[a + Un]
=
2
n
[U1+ Un ].
If, we expanding the formula Sn =
2
n
[2a + (n-1)b], we will obtain:
Sn =
2
n
[2a + (n-1)b]=
2
n
(2a + bn – b) =
2
n
n2 + n
ba
2
2 
Questions:
1. Find the sum of first 99 terms of 3+5+7+….
2. Find the sum of first 999 terms of 4+8+12+….
3. Calculate 2+4+6+…+122
4. Calculate the sum of all integers from 1 to 1000
5. Given that the sum of the first n terms of an arithmetic series is Sn = 3n2-7n.
find the formula of the n-th term of the series!