Difference between revisions of "Types of progressions"

From Karnataka Open Educational Resources
Jump to navigation Jump to search
 
(41 intermediate revisions by 4 users not shown)
Line 1: Line 1:
 +
<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#ffffff; vertical-align:top; text-align:center; padding:5px;">
 +
''[http://karnatakaeducation.org.in/KOER/೧೦ನೇ_ತರಗತಿಯ_ಶ್ರೇಢಿಯ_ವಿಧಗಳು ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ]''</div>
 +
 
<!-- This portal was created using subst:box portal skeleton  -->
 
<!-- This portal was created using subst:box portal skeleton  -->
 
<!--        BANNER ACROSS TOP OF PAGE        -->
 
<!--        BANNER ACROSS TOP OF PAGE        -->
 
{| id="mp-topbanner" style="width:100%;font-size:100%;border-collapse:separate;border-spacing:20px;"
 
{| id="mp-topbanner" style="width:100%;font-size:100%;border-collapse:separate;border-spacing:20px;"
 
|-
 
|-
−
|style="width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
+
| style="width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |
 
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics]
 
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics]
−
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Philosophy Philosophy of Mathematics]
+
| style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Philosophy Philosophy of Mathematics]
−
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
+
| style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |
 
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Pedagogy Teaching of Mathematics]
 
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Pedagogy Teaching of Mathematics]
−
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
+
| style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |
 
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus]
 
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus]
−
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
+
| style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |
 
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Topics Topics in School Mathematics]
 
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Topics Topics in School Mathematics]
−
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
+
| style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |
 
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Text_Books#Mathematics_-_Textbooks Textbooks]
 
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Text_Books#Mathematics_-_Textbooks Textbooks]
−
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
+
| style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |
 
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank]
 
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank]
 
|}
 
|}
Line 21: Line 24:
 
= Concept Map =
 
= Concept Map =
 
__FORCETOC__
 
__FORCETOC__
−
<mm>[[Types of progressions.mm|Flash]]</mm>
+
 
 +
[[File:Types of progressions.mm|Flash]]
  
 
= Textbook =
 
= Textbook =
Line 33: Line 37:
 
#[http://www.mathsisfun.com/algebra/sequences-sums-geometric.html Maths is fun for Geometric progressions]
 
#[http://www.mathsisfun.com/algebra/sequences-sums-geometric.html Maths is fun for Geometric progressions]
 
#[http://www.mathisfunforum.com/viewtopic.php?id=3305 maths is fun all three types progression]
 
#[http://www.mathisfunforum.com/viewtopic.php?id=3305 maths is fun all three types progression]
 +
Quiz Websites
 +
#[http://www.projectmaths.ie/students/cd-strand3LC/arithmeticsequence.htm Quiz for Arithmetic Progressions]
 +
#[http://www.cliffsnotes.com/math/algebra/algebra-ii/sequences-and-series/quiz-arithmetic-sequence Quiz for AP and GP]
  
 
==Reference Books==
 
==Reference Books==
Line 47: Line 54:
 
==Concept #1 Arithmetic Progression==
 
==Concept #1 Arithmetic Progression==
 
===Learning objectives===
 
===Learning objectives===
 +
#Definition of Arithmetic progression
 +
#Writing the general form of an A.P
 +
#Terms used in A.P
 +
#Finding 'a', common difference, 'n' th  of A.P
 +
#Framing formula to find the sum of a finite arithmetic series.
 +
#Finding the sum of a finite arithmetic series.
 +
 
===Notes for teachers===
 
===Notes for teachers===
−
''These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.''
+
#An arithmetic progression is a sequence in which each term is obtained by adding a fixed number to the preceding term.
 +
#General form : a , a+d , a+2d , a+3d, . . . . ., a+(n-1)d
 +
#Common Difference (d) : Difference between any term and its preceding term
 +
# Formula's of Arithmetic progression
  
 
===Activities===
 
===Activities===
  
−
#Activity No #1
+
#Activity No #1 activity for arithmetic progression
−
#Activity No #2
+
#Activity No #2 activity for arithmetic progression
−
 
 
  
 
==Concept #2 Harmonic progression==
 
==Concept #2 Harmonic progression==
 
===Learning objectives===
 
===Learning objectives===
 +
#Defining an Harmonic progression
 +
#The General form of Harmonic Progression
 +
#Compare H.P with other type of progression
 +
#Identifying H.P among a given set of progression
 +
 
===Notes for teachers===
 
===Notes for teachers===
−
''These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.''
+
A sequence in which , the reciprocals of the terms form an arithmetic progression is called a Harmonic progression.
−
 
 
  
 
===Activities===
 
===Activities===
−
#Activity No #1 '''Concept Name - Activity No.'''
+
#Activity No #1 acivity for Harmonic progression
−
#Activity No #2 '''Concept Name - Activity No.'''
+
#Activity No #2 acivity for Harmonic progression
−
''
 
  
 
==Concept #3 Geometric progression==
 
==Concept #3 Geometric progression==
 
===Learning objectives===
 
===Learning objectives===
 +
#Defining G.P by recognizing common ratios
 +
#General form of G.P
 +
#Terms used in G.P
 +
#Identifying next term and precedig term of an 'n' th term of G.P
 +
#Finding the common ratio, a specific term and the last term of G.P
 +
#Formulating the formula 'n'th term of G.P , sum formula based on 'r', Sum of infinite formula,
 +
 
===Notes for teachers===
 
===Notes for teachers===
−
''These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.''
+
# A geometric progression is a sequence in which each succeeding term is obtained by multiplying the preceding term by a fixed number.
−
 
+
#The ratio of a term and its preceeding term is called common ratio (r).
  
 
===Activities===
 
===Activities===
−
#Activity No #1 '''Concept Name - Activity No.'''
+
#Activity No #1 activity for Geometric progression
−
#Activity No #2 '''Concept Name - Activity No.'''
+
#Activity No #2 activity for Geometric progression
−
''
 
−
 
 
−
== Headline text ==
 
  
 
==Concept #4 Relation between A.M, G.M, H.M==
 
==Concept #4 Relation between A.M, G.M, H.M==
 
===Learning objectives===
 
===Learning objectives===
 +
#Formulating the formula for A.M, G.M and H.M
 +
#Using formula to find mean of any two terms in A.P , G.P and H.P
 +
#Relation between A.M , G.M and H.M
 +
 
===Notes for teachers===
 
===Notes for teachers===
−
''These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.''
+
#Arithmetic mean of two numbers is equal to half of their sum.
−
 
+
#The harmonic mean of any two numbers is equal to twice their product divided by their sum.
 +
#The Geometric mean of any numbers is square root of their product.
 +
#Geometric mean is equal to square root of their product of arithmetic mean and harmonic mean/
  
 
===Activities===
 
===Activities===
−
#Activity No #1 '''Concept Name - Activity No.'''
+
#Activity No #1 activity to show relation between A.M, G.M, H.M
−
#Activity No #2 '''Concept Name - Activity No.'''
+
#Activity No #2 activity to show relation between A.M, G.M, H.M
−
''
 
−
 
 
−
== Headline text ==
 
  
 
=Assessment activities for CCE=
 
=Assessment activities for CCE=
  
 
= Hints for difficult problems =
 
= Hints for difficult problems =
 +
1. A company employed 400 persons in the year 2001 and each year increased by 35 persons. In which year the number of employees in the company will be 785?
 +
[[Class10_progressions_problems#Problem_1_from_Exercise_3.2_.28_Q.N.11_-_page_No._37.29|click here for Solution]]<br>
 +
2. The sum of 6 terms which form an A.P is 345. The difference between the first and last terms is 55. Find the terms.
 +
[[Class10_progressions_problems#Problem_2_from_Exercise_3.3_.28_Q.N.12_-_page_No._43.29|click here for solution]]<br>
 +
3. Find two numbers whose arithmetic mean exceeds their geometric mean by 2, and whose harmonic mean is one-fifth of the larger number .[[Class10_progressions_problems#Problem 3|click here for solution]]<br>
 +
4. If 'a' be the arithmetic mean between 'b' and 'c', and 'b' the geometric mean between 'a' and 'c', then prove that 'c' will be the harmonic mean between 'a' and 'b'.[[Class10_progressions_problems#Problem 4|click here for solution]]
  
 
= Project Ideas =
 
= Project Ideas =
  
 
= Math Fun =
 
= Math Fun =
 +
 +
[[Category:Progressions]]

Latest revision as of 04:01, 12 November 2019

ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ

The Story of Mathematics

Philosophy of Mathematics

Teaching of Mathematics

Curriculum and Syllabus

Topics in School Mathematics

Textbooks

Question Bank

While creating a resource page, please click here for a resource creation checklist.

Concept Map

[maximize]

Textbook

  1. Gujarat textbook for class 10 : Chapter 5 Arithmetic progression
  2. Kerala state textbook for class 10 : Chapter 01 Arithmetic Sequences
  3. NCERT text book : Aarithmetic progression

Additional Information

Useful websites

  1. Maths is fun for Arithmetic progressions
  2. Maths is fun for Geometric progressions
  3. maths is fun all three types progression

Quiz Websites

  1. Quiz for Arithmetic Progressions
  2. Quiz for AP and GP

Reference Books

Teaching Outlines

  1. Identify the types of progression in the given sequence
  2. Meaning of three types of progression
  3. General form of three types of progression
  4. Difference between three types of progression
  5. Terms related to A.P , H.P and G.P
  6. Formula's of three types progression
  7. Mean of three types of progression and their relation
  8. Problems of three types of progression

Concept #1 Arithmetic Progression

Learning objectives

  1. Definition of Arithmetic progression
  2. Writing the general form of an A.P
  3. Terms used in A.P
  4. Finding 'a', common difference, 'n' th of A.P
  5. Framing formula to find the sum of a finite arithmetic series.
  6. Finding the sum of a finite arithmetic series.

Notes for teachers

  1. An arithmetic progression is a sequence in which each term is obtained by adding a fixed number to the preceding term.
  2. General form : a , a+d , a+2d , a+3d, . . . . ., a+(n-1)d
  3. Common Difference (d) : Difference between any term and its preceding term
  4. Formula's of Arithmetic progression

Activities

  1. Activity No #1 activity for arithmetic progression
  2. Activity No #2 activity for arithmetic progression

Concept #2 Harmonic progression

Learning objectives

  1. Defining an Harmonic progression
  2. The General form of Harmonic Progression
  3. Compare H.P with other type of progression
  4. Identifying H.P among a given set of progression

Notes for teachers

A sequence in which , the reciprocals of the terms form an arithmetic progression is called a Harmonic progression.

Activities

  1. Activity No #1 acivity for Harmonic progression
  2. Activity No #2 acivity for Harmonic progression

Concept #3 Geometric progression

Learning objectives

  1. Defining G.P by recognizing common ratios
  2. General form of G.P
  3. Terms used in G.P
  4. Identifying next term and precedig term of an 'n' th term of G.P
  5. Finding the common ratio, a specific term and the last term of G.P
  6. Formulating the formula 'n'th term of G.P , sum formula based on 'r', Sum of infinite formula,

Notes for teachers

  1. A geometric progression is a sequence in which each succeeding term is obtained by multiplying the preceding term by a fixed number.
  2. The ratio of a term and its preceeding term is called common ratio (r).

Activities

  1. Activity No #1 activity for Geometric progression
  2. Activity No #2 activity for Geometric progression

Concept #4 Relation between A.M, G.M, H.M

Learning objectives

  1. Formulating the formula for A.M, G.M and H.M
  2. Using formula to find mean of any two terms in A.P , G.P and H.P
  3. Relation between A.M , G.M and H.M

Notes for teachers

  1. Arithmetic mean of two numbers is equal to half of their sum.
  2. The harmonic mean of any two numbers is equal to twice their product divided by their sum.
  3. The Geometric mean of any numbers is square root of their product.
  4. Geometric mean is equal to square root of their product of arithmetic mean and harmonic mean/

Activities

  1. Activity No #1 activity to show relation between A.M, G.M, H.M
  2. Activity No #2 activity to show relation between A.M, G.M, H.M

Assessment activities for CCE

Hints for difficult problems

1. A company employed 400 persons in the year 2001 and each year increased by 35 persons. In which year the number of employees in the company will be 785? click here for Solution
2. The sum of 6 terms which form an A.P is 345. The difference between the first and last terms is 55. Find the terms. click here for solution
3. Find two numbers whose arithmetic mean exceeds their geometric mean by 2, and whose harmonic mean is one-fifth of the larger number .click here for solution
4. If 'a' be the arithmetic mean between 'b' and 'c', and 'b' the geometric mean between 'a' and 'c', then prove that 'c' will be the harmonic mean between 'a' and 'b'.click here for solution

Project Ideas

Math Fun

Retrieved from "https://karnatakaeducation.org.in/KOER/en/index.php?title=Types_of_progressions&oldid=32634"