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Arithmetic
sequence
and
geometric
sequence
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Contents of this Template
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585&ei=F_
Progress:
Arithmetic
sequence
Geometric
sequence
19 , 27 , 35 , 43 , 51 , …
Give an example of
Common difference :
8
14 , 42 , 126 , 378 , …
Common ratio : 3
Differentiates a
geometric
sequence from an
arithmetic sequence
(M10AL-Id-2)
—learning competencies
Identify a
sequence
as
arithmetic
or
geometric;
01
Demonstrate appreciation of
recognizing patterns of
differentiating geometric from
arithmetic sequence.
03
Differentiate
a geometric
sequence
from
arithmetic
sequence;
and
02
Learning objectives :
gro
up
wor
01
6 , 18 , 54 ,
162 , …
01
GEOMETRIC SEQUENCE
Common ratio = 3
4 , 10 , 16 ,
22 , …
02
ARITHMETIC SEQUENCE
Common difference = 6
1 , 1 , 2 , 3 , 5
, 8 , …
03
NEITHER
5 , 25 , 125 ,
625 , …
04
GEOMETRIC SEQUENCE
Common ratio = 5
5 , 8 , 13 ,
21 , 34…
05
NEITHER
QUESTIONS:
CREDITS: This presentation template was
created by Slidesgo, including icons by Flaticon,
and infographics & images by Freepik
By
PAI
R!
compare and contrast arithmetic and geometric
sequences using a two-column chart.
arithmetic geometric
With common difference With common ratio
Adding a constant called
common difference
Multiplying a constant called
common ratio
to get the common difference,
subtract the last term to the
precede term
to get the common ratio, divide
the last term to the precede
term
+ - x ÷
Indivi
dual
work..
.
6 , 11 , 16 , 21 ,
26 , 31
ARITHMETIC SEQUENCE
d = 5
1 , 8 , 15 , 21 ,
29
NEITHER
10, 50, 250,
1250, …
GEOMETRIC SEQUENCE
r = 5
5 , 10 , 15 , 20
, 25
ARITHMETIC SEQUENCE
d = 5
31.25 , 62.5 , 125
, 250 , 500
GEOMETRIC SEQUENCE
r = 2
Seating around
tables. Think
about a
restaurant. A
square table fits 4
people. When two
square tables are
put together, now
6 people are
seated. Put 3
square tables
together and now
8 people are
Arithmetic sequence in real life
https://www.google.com/url?
sa=i&url=https%3A%2F
%2Ftimefliesedu.com%
Pyramid-like
patterns, where
objects are
increasing or
decreasing in a
constant manner.
Ideas for this are
seats in a stadium
or an auditorium.
Arithmetic sequence in real life
https://www.google.com/url?sa=i&url=https%3A
%2F%2Ftimefliesedu.com
%2F2019%2F12%2F17%2Fexamples-of-real-
life-arithmetic-sequences%2
A ball
bouncing is
an example
of finite
geometric
sequence.
Geometric sequence in real life
https://www.google.com/url?
sa=i&url=https%3A%2F
%2Fwww.istockphoto.com%2Fphotos
%2Fbasketball-bouncing&psig=
Mone
y in
the
bank.
Geometric sequence in real life
https://
www.google.com/
url?sa=i&url=https
%3A%2F
%2Fwww.linkedin.c
om%2Fpulse
%2Fjourney-
accumulating-
wealth-starts-from-
today-habit-savings-
singh&psi
https://
www.google.com/
url?sa=i&url=https
%3A%2F
%2Fwww.sofi.com
%2Flearn
%2Fcontent
%2Fdifficulty-of-
saving-money
%2F&ps
“On summer vacation, Bird’s Café of Banate, Malungon,
Sarangani Province is in need of part-timers .Since its
vacation, you decided to apply for a job. You are given
two options for your salary.
Option A, Php 50 1st day, Php 52 for 2nd
day, Php54 for
3rd
day and so on.
Option B, Php 10 the first day, Php20 the second
day ,Php40 the third day and so on.
How much is your salary after 10 working days if you
choose option A? Option B?
Which is a better option?
Quiz #6: solve the problem
10, 20, 40, 80, 60, 120, 240, 480, 960,
1920
Arithmetic
sequence
50, 52, 54, 56, 58, 60, 62, 64, 66, 68
Geometric
sequence
About the data i’ve found
Option a
Option B in better than Option
A.
Option b
ASSIGN
MENT!!!
Memorize the
multiplication
table 6 to 10
Linear interpolation solution
steps
Step #01
Arrange the no. in
ascending order.
Step #02
Locate the position
of the score in the
distribution.
Step #03
Find the difference
between the 2
values wherein is
situated.
Step #04
Get the decimal part
result in step 2 and
multiply it with the
result in step 3
Step #05
Add the result in step 4 to the smallest no. in step 3 to get
the value of .
These are the scores of 13 students in grade
10 dura in a 20 item test. Find
3 , 7, 9, 11, 15, 18, 19, 15, 14, 14, 17, 20, 20
Step #01
Arrange the no. in
ascending order.
3, 7, 9, 11, 14, 14, 15, 15, 17, 18, 19, 20, 20
Step #02
Locate the position of
the score in the
distribution.
𝑸𝒌=
𝒌(𝒏+𝟏)
𝟒
𝑸𝟏=
𝟏(𝟏𝟑+𝟏)
𝟒
𝑸𝟏=
𝟏(𝟏𝟒)
𝟒
𝑸𝟏=
𝟏𝟒
𝟒
𝑸𝟏=𝟑.𝟓𝒕𝒉
Step #03
Find the difference
between the 2
values wherein is
situated.
𝟏𝟏−𝟗=𝟐
Step #04
Get the decimal part
result in step 2 and
multiply it with the
result in step 3
(𝟎.𝟓)(𝟐)=𝟏
Step #05
Add the result in step 4 to
the smallest no. in step 3
to get the value of .
𝟏+𝟗=𝟏𝟎
𝒕𝒉𝒆𝒓𝒆𝒇𝒐𝒓𝒆𝑄1=𝟏𝟎
– is a sequence where
each term is found by
multiplying or dividing
the same value from one
term to the next. We call
this value “common
ratio”.
geometric sequence
Progress:
Denoted
as (r)
r = any term
precedes
Tip: The initial letter of their name is also the
initial letter of the country they come from
Progress:
1, 2, 4, 8, 16
Term:
Geometric Sequence:
Common ration:
1
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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
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Ana Robin Finnick
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Ana
Math
Finnick hates math although he is good
at it
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!
Collect
ing
evide
nce
03
Here you can describe the
content of the section
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
REFERENC
E
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:
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:
Solut
ion
foun
d!
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
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geometric vs arithmetic sequence mathematic 10
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JANUARY FEBRUARY MARCH APRIL MAY JUNE
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geometric vs arithmetic sequence mathematic 10
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geometric vs arithmetic sequence mathematic 10

  • 3. Contents of this Template https://www.google.com/search? q=REVIEW&sca_esv=0381ce655eb7fe96&rlz=1C1GCEA_enPH1121PH1121&udm=2&biw=1280&bih= 585&ei=F_
  • 4. Progress: Arithmetic sequence Geometric sequence 19 , 27 , 35 , 43 , 51 , … Give an example of Common difference : 8 14 , 42 , 126 , 378 , … Common ratio : 3
  • 5. Differentiates a geometric sequence from an arithmetic sequence (M10AL-Id-2) —learning competencies
  • 6. Identify a sequence as arithmetic or geometric; 01 Demonstrate appreciation of recognizing patterns of differentiating geometric from arithmetic sequence. 03 Differentiate a geometric sequence from arithmetic sequence; and 02 Learning objectives :
  • 8. 6 , 18 , 54 , 162 , … 01 GEOMETRIC SEQUENCE Common ratio = 3
  • 9. 4 , 10 , 16 , 22 , … 02 ARITHMETIC SEQUENCE Common difference = 6
  • 10. 1 , 1 , 2 , 3 , 5 , 8 , … 03 NEITHER
  • 11. 5 , 25 , 125 , 625 , … 04 GEOMETRIC SEQUENCE Common ratio = 5
  • 12. 5 , 8 , 13 , 21 , 34… 05 NEITHER
  • 14. CREDITS: This presentation template was created by Slidesgo, including icons by Flaticon, and infographics & images by Freepik By PAI R!
  • 15. compare and contrast arithmetic and geometric sequences using a two-column chart. arithmetic geometric With common difference With common ratio Adding a constant called common difference Multiplying a constant called common ratio to get the common difference, subtract the last term to the precede term to get the common ratio, divide the last term to the precede term + - x ÷
  • 17. 6 , 11 , 16 , 21 , 26 , 31 ARITHMETIC SEQUENCE d = 5
  • 18. 1 , 8 , 15 , 21 , 29 NEITHER
  • 19. 10, 50, 250, 1250, … GEOMETRIC SEQUENCE r = 5
  • 20. 5 , 10 , 15 , 20 , 25 ARITHMETIC SEQUENCE d = 5
  • 21. 31.25 , 62.5 , 125 , 250 , 500 GEOMETRIC SEQUENCE r = 2
  • 22. Seating around tables. Think about a restaurant. A square table fits 4 people. When two square tables are put together, now 6 people are seated. Put 3 square tables together and now 8 people are Arithmetic sequence in real life https://www.google.com/url? sa=i&url=https%3A%2F %2Ftimefliesedu.com%
  • 23. Pyramid-like patterns, where objects are increasing or decreasing in a constant manner. Ideas for this are seats in a stadium or an auditorium. Arithmetic sequence in real life https://www.google.com/url?sa=i&url=https%3A %2F%2Ftimefliesedu.com %2F2019%2F12%2F17%2Fexamples-of-real- life-arithmetic-sequences%2
  • 24. A ball bouncing is an example of finite geometric sequence. Geometric sequence in real life https://www.google.com/url? sa=i&url=https%3A%2F %2Fwww.istockphoto.com%2Fphotos %2Fbasketball-bouncing&psig=
  • 25. Mone y in the bank. Geometric sequence in real life https:// www.google.com/ url?sa=i&url=https %3A%2F %2Fwww.linkedin.c om%2Fpulse %2Fjourney- accumulating- wealth-starts-from- today-habit-savings- singh&psi https:// www.google.com/ url?sa=i&url=https %3A%2F %2Fwww.sofi.com %2Flearn %2Fcontent %2Fdifficulty-of- saving-money %2F&ps
  • 26. “On summer vacation, Bird’s Café of Banate, Malungon, Sarangani Province is in need of part-timers .Since its vacation, you decided to apply for a job. You are given two options for your salary. Option A, Php 50 1st day, Php 52 for 2nd day, Php54 for 3rd day and so on. Option B, Php 10 the first day, Php20 the second day ,Php40 the third day and so on. How much is your salary after 10 working days if you choose option A? Option B? Which is a better option? Quiz #6: solve the problem
  • 27. 10, 20, 40, 80, 60, 120, 240, 480, 960, 1920 Arithmetic sequence 50, 52, 54, 56, 58, 60, 62, 64, 66, 68 Geometric sequence About the data i’ve found Option a Option B in better than Option A. Option b
  • 29. Linear interpolation solution steps Step #01 Arrange the no. in ascending order. Step #02 Locate the position of the score in the distribution. Step #03 Find the difference between the 2 values wherein is situated. Step #04 Get the decimal part result in step 2 and multiply it with the result in step 3 Step #05 Add the result in step 4 to the smallest no. in step 3 to get the value of .
  • 30. These are the scores of 13 students in grade 10 dura in a 20 item test. Find 3 , 7, 9, 11, 15, 18, 19, 15, 14, 14, 17, 20, 20 Step #01 Arrange the no. in ascending order. 3, 7, 9, 11, 14, 14, 15, 15, 17, 18, 19, 20, 20 Step #02 Locate the position of the score in the distribution. 𝑸𝒌= 𝒌(𝒏+𝟏) 𝟒 𝑸𝟏= 𝟏(𝟏𝟑+𝟏) 𝟒 𝑸𝟏= 𝟏(𝟏𝟒) 𝟒 𝑸𝟏= 𝟏𝟒 𝟒 𝑸𝟏=𝟑.𝟓𝒕𝒉 Step #03 Find the difference between the 2 values wherein is situated. 𝟏𝟏−𝟗=𝟐 Step #04 Get the decimal part result in step 2 and multiply it with the result in step 3 (𝟎.𝟓)(𝟐)=𝟏 Step #05 Add the result in step 4 to the smallest no. in step 3 to get the value of . 𝟏+𝟗=𝟏𝟎 𝒕𝒉𝒆𝒓𝒆𝒇𝒐𝒓𝒆𝑄1=𝟏𝟎
  • 31. – is a sequence where each term is found by multiplying or dividing the same value from one term to the next. We call this value “common ratio”. geometric sequence Progress: Denoted as (r) r = any term precedes
  • 32. Tip: The initial letter of their name is also the initial letter of the country they come from Progress: 1, 2, 4, 8, 16 Term: Geometric Sequence: Common ration: 1
  • 33. Contents of this Template Here’s what you’ll find in this Slidesgo template: 1. A slide structure based on an educational presentation for high school, which you can easily adapt to your needs. For more info on how to edit the template, please visit Slidesgo School or read our FAQs. 2. An assortment of graphic resources that are suitable for use in the presentation can be found in the alternative resources slide. 3. A thanks slide, which you must keep so that proper credits for our design are given. 4. A resources slide, where you’ll find links to all the elements used in the template. 5. Instructions for use 6. Final slides with: ● The fonts and colors used in the template. ● A selection of illustrations. You can also customize and animate them as you wish with the online editor. Visit Storyset to find more. ● More infographic resources, whose size and color can be edited. ● Sets of customizable icons of the following themes: general, business, avatar, creative process, education, help & support, medical, nature, performing arts, SEO & marketing, and teamwork. You can delete this slide when you’re done editing the presentation.
  • 34. 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
  • 35. This is robin Progress: Special traits Tall, no freckles, smiley and fun nationality Unknown hobbies Soccer, rugby and football
  • 36. 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
  • 37. 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!
  • 38. Collect ing evide nce 03 Here you can describe the content of the section
  • 39. 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
  • 40. REFERENC E 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:
  • 41. 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:
  • 42. Solut ion foun d! Here you can describe the content of the section 04
  • 43. 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:
  • 44. 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:
  • 48. Alternative Resources Photos: ● Ruler with rubber percentages Vectors: ● Creative maze for kids worksheet ● Hand drawn school infographic elements pack ● Realistic math chalkboard background ● A person in different ages design ● Hand drawn black girl in different poses ● Hand drawn people avatar collection ● Back to school instagram stories set ● Travel pattern with elements Icons: ● Human Mind
  • 49. Resources Did you like the resources of this template? Get them for free at our other websites! Photos: ● Colourful statistical pie charts for science fractions ● School stationery blue items copy space background ● Colourful math numbers and fractions Vectors: ● Cute counting game with school elements ● Maze for kids with pirate and treasure ● Character poses with skateboarder Icons: ● Back to school ● Adventure
  • 50. Instructions for use (free users) In order to use this template, you must credit Slidesgo by keeping the Thanks slide. You are allowed to: ● Modify this template. ● Use it for both personal and commercial purposes. You are not allowed to: ● Sublicense, sell or rent any of Slidesgo Content (or a modified version of Slidesgo Content). ● Distribute this Slidesgo Template (or a modified version of this Slidesgo Template) or include it in a database or in any other product or service that offers downloadable images, icons or presentations that may be subject to distribution or resale. ● Use any of the elements that are part of this Slidesgo Template in an isolated and separated way from this Template. ● Delete the “Thanks” or “Credits” slide. ● Register any of the elements that are part of this template as a trademark or logo, or register it as a work in an intellectual property registry or similar. For more information about editing slides, please read our FAQs or visit Slidesgo School: https://slidesgo.com/faqs and https://slidesgo.com/slidesgo-school
  • 51. Instructions for use (premium users) In order to use this template, you must be a Premium user on Slidesgo. You are allowed to: ● Modify this template. ● Use it for both personal and commercial purposes. ● Hide or delete the “Thanks” slide and the mention to Slidesgo in the credits. ● Share this template in an editable format with people who are not part of your team. You are not allowed to: ● Sublicense, sell or rent this Slidesgo Template (or a modified version of this Slidesgo Template). ● Distribute this Slidesgo Template (or a modified version of this Slidesgo Template) or include it in a database or in any other product or service that offers downloadable images, icons or presentations that may be subject to distribution or resale. ● Use any of the elements that are part of this Slidesgo Template in an isolated and separated way from this Template. ● Register any of the elements that are part of this template as a trademark or logo, or register it as a work in an intellectual property registry or similar. For more information about editing slides, please read our FAQs or visit Slidesgo School: https://slidesgo.com/faqs and https://slidesgo.com/slidesgo-school
  • 52. Fonts & colors used This presentation has been made using the following fonts: Bahiana (https://fonts.google.com/specimen/Bahiana) Didact Gothic (https://fonts.google.com/specimen/Didact+Gothic) #72b5ca #a8e1f2 #9f7494 #629cae #e6c7de #c44253 #ff657d #b885ab #fac539 #ffe15f
  • 53. Storyset Create your Story with our illustrated concepts. Choose the style you like the most, edit its colors, pick the background and layers you want to show and bring them to life with the animator panel! It will boost your presentation. Check out How it Works. Pana Amico Bro Rafiki Cuate
  • 54. You can easily resize these resources without losing quality. To change the color, just ungroup the resource and click on the object you want to change. Then, click on the paint bucket and select the color you want. Group the resource again when you’re done. You can also look for more infographics on Slidesgo. Use our editable graphic resources...
  • 57. 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
  • 60. ...and our sets of editable icons You can resize these icons without losing quality. You can change the stroke and fill color; just select the icon and click on the paint bucket/pen. In Google Slides, you can also use Flaticon’s extension, allowing you to customize and add even more icons.
  • 63. Help & Support Icons Avatar Icons
  • 64. Creative Process Icons Performing Arts Icons