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Baris dan deret
Pengertian
a) Barisan adalah Barisan merupakan suatu runtutan angka (u1,u2,u3,…) atau bilangan dari kiri ke kanan dengan
pola serta aturan tertentu (Un=F(n), dengan n= 1,2,3,…)
Contoh: 1,3,5,7,9, adalah barisan dengan Un= 2n-1
3,6,12,24,… adalah barisan dengan Un= 3xrn-1
 Barisan Infinite merupakan barisan tak hingga
 Barisan finite merupakan barisan yang memiliki Batasan atau aturan tertentu
b) Deret dibentuk dari penjumlahan atau pengurangan dari suku barisan
Contoh : barisan :3,4,6,9,..
deret :3+4+6+9+…
a) Notasi Sigma(∑)
● Di dalam bentuk suatu persamaan suatu deret dapat dituliskan dalam bentuk notasi sigma
● Misal pada deret 1+3+5+7 dengan rumus Un= 2n-1 kita dapat tulis dengan notasi sigma
𝑛=1
4
2𝑛 − 1
Deret Aritmatika
Three friends –Ana, Robin and
Finnick– are 48 years old in total.
Knowing that Robin is two times older
than Ana and Finnick is 15… How old
are them and where is Finnick from?
Tip: The initial letter of their name is also the initial
letter of the country they come from
Progress:
iNTROducing
ourselves
01
Here you can describe the content of the section
Welcome to our Math Mystery Escape Room!!
Here, you will find that Venus has a beautiful
name and is the second planet from the Sun. It’s
terribly hot, even hotter than Mercury, and its
atmosphere is extremely poisonous
About the introduction
Progress:
She is a very funny Turkish girl. She
enjoys reading, playing with her dogs
and visiting her partner every
weekend. She is specially good in
psychology and mathematics as she
has a very analytical mind. Her friends
describe her as loyal and loving
This is ana
Progress:
We don’t know where he is from
Progress:
This is finnick!
He is 15 years old
Finnick loves chess and parkour
He does not have lots of friends: only 1
He has a tortoise called Edison
He hates math but is good at them
Finnick has always a smile on his face
This is robin
Progress:
Special traits
Tall, no freckles, smiley and fun
nationality
Unknown
hobbies
Soccer, rugby and football
gathering the data
Progress:
80
60
40
20
0
Ana Robin Finnick
To modify this graph, click on it, follow the link, change the data with your own and replace the graph in this slide
Her strong: be punctual
Ana “O’clock” is an excellent organizer
Books and knowledge
Robin loves to read, almost as much as Ana
Math
Finnick hates math although he is good at it
Understanding it
02 Here you can describe the
content of the section
utilities for deciphering this math mystery
Progress:
SOME RANDOM NOTES
It is important to have
somewhere to write
Talk to my teacher
Your math teachers are
the best! They know it
all
HANDY NOTEBOOK
Afterwards, put all your
notes in the same place
A PRIZE TO WIN!
Will you be the first to
decipher the mystery?
Progress:
THERE CAN BE TWO PATHS...
BUT ONLY ONE HAS THE SOLUTION
It’s OK if you have different paths for
solving a math problem. Hooray:
You’re actually on the right track!
It may come to you just in the verge
of giving up, so keep trying. You will
find the answer if you are prepared!
Are you STUCK?
Steps to understand it
Progress:
Step #01
Ceres is located in
the asteroid belt
Step #02
Pluto is considered a
dwarf planet
Step #03
Earth is the planet
where we live on
Step #04
Saturn is a gas giant
and has rings
Mathematics is not about
numbers, equations,
computations or algorithms: it
is about understanding.
—SOMEONE FAMOUS
We must understand HIS origin
Progress:
Is HE american?
The problem asked
about Finnick, not Ana...
Or argentinian?
On second thought,
Argentina is discarded
no, IS HE finnish?
Yes, definitely Finnish:
it matches the first
letter!
Or maybe turkish!
This is tricky because it
is in between!
Collecting
evidence
03
Here you can describe the
content of the section
Or maybe these?
13, 20, 15
Will these be the ages?
15, 18, 15
Progress:
About the data i’ve found
positive negative
45% 55%
Earth is the
planet we live on
Pluto is now a
dwarf planet
2nd attempt
9, 24, 15
Progress:
1st attempt
6, 27, 15 15, 19, 15
3rd attempt
13, 21, 15
4th attempt
9th attempt
4, 29, 15
10th attempt
16, 18, 15
11th attempt
5, 28, 15
5th attempt
8, 25, 15
6th attempt
10, 23, 15
7th attempt
7, 26, 15
8th attempt
14, 20, 15
Attempts made OVER TIME
So many
solutions!
Which is the
correct one?
Objects in my investigation
Progress:
item description availability
Knowledge Mercury is the closest planet to the Sun
Reliable pen Venus has actually a very beautiful name
World map Earth is the third planet from the Sun
Victory badge Despite being red, Mars is a cold place
REFERENCE
Ceres is located in
the asteroid belt
Evidence found
ANCIENT NOTES
Pluto is considered a
dwarf planet
EVIDENCE
Earth is the planet
where we live on
MODERN NOTES
Saturn is a gas giant
and has rings
Progress:
Let’s see what
we have found...
Is it female...
Despite being red,
Mars is a cold place
Or male?
This is the planet
where we all live on
magnetism
It was named after
the Roman god
School potion
Jupiter is a gas giant
and the biggest
School clock
Venus is the second
planet from the Sun
School bell
Pluto is considered a
dwarf planet
Gathering evidence
Progress:
Solution
found!
Here you can describe the
content of the section
04
Have you found the solution on your computer?
I have not! However, you can
actually change the image on the
screen with your own by replacing
it and uploading a photo from your
own computer! Awesome!
Progress:
No way! However, you can actually
change the image on the screen
with your own by replacing it and
uploading a photo from your own
computer! Awesome!
Or, maybe, on your tablet?
Progress:
Hooray! I’m almost there! Bear in
mind that you can change the
image on the screen with your own
by replacing it and uploading a
photo from your own computer!
Nope, it’s on my phone! Let’s see what it is!
Progress:
Ana is 11, robin 22 and finnick 15
Yay! And Finnick is from Finland!
CREDITS: This presentation template was created by
Slidesgo, including icons by Flaticon, and
infographics & images by Freepik
THANKS a lot!
Do you have any questions?
addyouremail@freepik.com
+91 620 421 838
yourcompany.com
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AlTernative icons
AlTernative progress icons
AlTernative math problems
AlTernative characters
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1029 - Danh muc Sach Giao Khoa 10 . pdf
 

baris dan deret

  • 1. Baris dan deret Pengertian a) Barisan adalah Barisan merupakan suatu runtutan angka (u1,u2,u3,…) atau bilangan dari kiri ke kanan dengan pola serta aturan tertentu (Un=F(n), dengan n= 1,2,3,…) Contoh: 1,3,5,7,9, adalah barisan dengan Un= 2n-1 3,6,12,24,… adalah barisan dengan Un= 3xrn-1  Barisan Infinite merupakan barisan tak hingga  Barisan finite merupakan barisan yang memiliki Batasan atau aturan tertentu b) Deret dibentuk dari penjumlahan atau pengurangan dari suku barisan Contoh : barisan :3,4,6,9,.. deret :3+4+6+9+… a) Notasi Sigma(∑) ● Di dalam bentuk suatu persamaan suatu deret dapat dituliskan dalam bentuk notasi sigma ● Misal pada deret 1+3+5+7 dengan rumus Un= 2n-1 kita dapat tulis dengan notasi sigma 𝑛=1 4 2𝑛 − 1
  • 3. Three friends –Ana, Robin and Finnick– are 48 years old in total. Knowing that Robin is two times older than Ana and Finnick is 15… How old are them and where is Finnick from? Tip: The initial letter of their name is also the initial letter of the country they come from Progress:
  • 4. iNTROducing ourselves 01 Here you can describe the content of the section
  • 5. Welcome to our Math Mystery Escape Room!! Here, you will find that Venus has a beautiful name and is the second planet from the Sun. It’s terribly hot, even hotter than Mercury, and its atmosphere is extremely poisonous About the introduction Progress:
  • 6. She is a very funny Turkish girl. She enjoys reading, playing with her dogs and visiting her partner every weekend. She is specially good in psychology and mathematics as she has a very analytical mind. Her friends describe her as loyal and loving This is ana Progress:
  • 7. We don’t know where he is from Progress: This is finnick! He is 15 years old Finnick loves chess and parkour He does not have lots of friends: only 1 He has a tortoise called Edison He hates math but is good at them Finnick has always a smile on his face
  • 8. This is robin Progress: Special traits Tall, no freckles, smiley and fun nationality Unknown hobbies Soccer, rugby and football
  • 9. gathering the data Progress: 80 60 40 20 0 Ana Robin Finnick To modify this graph, click on it, follow the link, change the data with your own and replace the graph in this slide Her strong: be punctual Ana “O’clock” is an excellent organizer Books and knowledge Robin loves to read, almost as much as Ana Math Finnick hates math although he is good at it
  • 10. Understanding it 02 Here you can describe the content of the section
  • 11. utilities for deciphering this math mystery Progress: SOME RANDOM NOTES It is important to have somewhere to write Talk to my teacher Your math teachers are the best! They know it all HANDY NOTEBOOK Afterwards, put all your notes in the same place A PRIZE TO WIN! Will you be the first to decipher the mystery?
  • 12. Progress: THERE CAN BE TWO PATHS... BUT ONLY ONE HAS THE SOLUTION It’s OK if you have different paths for solving a math problem. Hooray: You’re actually on the right track! It may come to you just in the verge of giving up, so keep trying. You will find the answer if you are prepared! Are you STUCK?
  • 13. Steps to understand it Progress: Step #01 Ceres is located in the asteroid belt Step #02 Pluto is considered a dwarf planet Step #03 Earth is the planet where we live on Step #04 Saturn is a gas giant and has rings
  • 14. Mathematics is not about numbers, equations, computations or algorithms: it is about understanding. —SOMEONE FAMOUS
  • 15. We must understand HIS origin Progress: Is HE american? The problem asked about Finnick, not Ana... Or argentinian? On second thought, Argentina is discarded no, IS HE finnish? Yes, definitely Finnish: it matches the first letter! Or maybe turkish! This is tricky because it is in between!
  • 16. Collecting evidence 03 Here you can describe the content of the section
  • 17. Or maybe these? 13, 20, 15 Will these be the ages? 15, 18, 15 Progress: About the data i’ve found positive negative 45% 55% Earth is the planet we live on Pluto is now a dwarf planet
  • 18. 2nd attempt 9, 24, 15 Progress: 1st attempt 6, 27, 15 15, 19, 15 3rd attempt 13, 21, 15 4th attempt 9th attempt 4, 29, 15 10th attempt 16, 18, 15 11th attempt 5, 28, 15 5th attempt 8, 25, 15 6th attempt 10, 23, 15 7th attempt 7, 26, 15 8th attempt 14, 20, 15 Attempts made OVER TIME
  • 19. So many solutions! Which is the correct one?
  • 20. Objects in my investigation Progress: item description availability Knowledge Mercury is the closest planet to the Sun Reliable pen Venus has actually a very beautiful name World map Earth is the third planet from the Sun Victory badge Despite being red, Mars is a cold place
  • 21. REFERENCE Ceres is located in the asteroid belt Evidence found ANCIENT NOTES Pluto is considered a dwarf planet EVIDENCE Earth is the planet where we live on MODERN NOTES Saturn is a gas giant and has rings Progress:
  • 22. Let’s see what we have found...
  • 23. Is it female... Despite being red, Mars is a cold place Or male? This is the planet where we all live on magnetism It was named after the Roman god School potion Jupiter is a gas giant and the biggest School clock Venus is the second planet from the Sun School bell Pluto is considered a dwarf planet Gathering evidence Progress:
  • 24. Solution found! Here you can describe the content of the section 04
  • 25. Have you found the solution on your computer? I have not! However, you can actually change the image on the screen with your own by replacing it and uploading a photo from your own computer! Awesome! Progress:
  • 26. No way! However, you can actually change the image on the screen with your own by replacing it and uploading a photo from your own computer! Awesome! Or, maybe, on your tablet? Progress:
  • 27. Hooray! I’m almost there! Bear in mind that you can change the image on the screen with your own by replacing it and uploading a photo from your own computer! Nope, it’s on my phone! Let’s see what it is! Progress:
  • 28. Ana is 11, robin 22 and finnick 15 Yay! And Finnick is from Finland!
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  • 43. JANUARY FEBRUARY MARCH APRIL MAY JUNE PHASE 1 PHASE 2 Task 1 Task 2 Task 1 Task 2 JANUARY FEBRUARY MARCH APRIL PHASE 1 Task 1 Task 2
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