Difference between revisions of "Types of progressions"
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==Concept #4 Relation between A.M, G.M, H.M== | ==Concept #4 Relation between A.M, G.M, H.M== |
Revision as of 12:34, 7 August 2014
Philosophy of Mathematics |
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Concept Map
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Textbook
- Gujarat textbook for class 10 : Chapter 5 Arithmetic progression
- Kerala state textbook for class 10 : Chapter 01 Arithmetic Sequences
- NCERT text book : Aarithmetic progression
Additional Information
Useful websites
- Maths is fun for Arithmetic progressions
- Maths is fun for Geometric progressions
- maths is fun all three types progression
Quiz Websites
Reference Books
Teaching Outlines
- Identify the types of progression in the given sequence
- Meaning of three types of progression
- General form of three types of progression
- Difference between three types of progression
- Terms related to A.P , H.P and G.P
- Formula's of three types progression
- Mean of three types of progression and their relation
- Problems of three types of progression
Concept #1 Arithmetic Progression
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
- 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
- Activity No #1
- Activity No #2
Concept #2 Harmonic progression
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
A sequence in which , the reciprocals of the terms form an arithmetic progression is called a Harmonic progression.
Activities
- Activity No #1 Concept Name - Activity No.
- Activity No #2 Concept Name - Activity No.
Concept #3 Geometric progression
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
- 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
- Activity No #1 Concept Name - Activity No.
- Activity No #2 Concept Name - Activity No.
Concept #4 Relation between A.M, G.M, H.M
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
- 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
- Activity No #1 Concept Name - Activity No.
- Activity No #2 Concept Name - Activity No.