arithmetic-vs-geometric.pptx

Arithmetic Sequences and Arithmetic Series – Basic Introduction
Arithmetic Sequences and Arithmetic Series – Basic Introduction

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 :

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By
PAIR!

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 ÷

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
seated.
Arithmetic sequence in real life

“On summer vacation, the packing Department of Patatas
Company of Tingub Mandaue City 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: 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

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
𝑄𝑘 𝑜𝑟 𝐷𝑘 𝑜𝑟 𝑃𝑘 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 𝑄𝑘 𝑜𝑟 𝐷𝑘 𝑜𝑟 𝑃𝑘.

These are the scores of 13 students in grade 10 dura in a 20 item test. Find 𝑸𝟏
3
,
7
,
9
,
11
,
15
,
18
,
19
,
15
,
14
,
14
,
17
,
20
,
20
Step #01
Arrange the no. in
ascending order.
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 𝑄1 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 𝑄1.
𝟏 + 𝟗 = 𝟏𝟎
𝒕𝒉𝒆𝒓𝒆𝒇𝒐𝒓𝒆 𝑄1 = 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”.
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:
Term:
Geometric Sequence:
Common ration:
1

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ANCIENT NOTES
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EVIDENCE
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MODERN NOTES
Saturn is a gas giant
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magnetism
It was named after
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School potion
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School clock
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School bell
Pluto is considered a
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