# Types of progressions

Philosophy of Mathematics |

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# Concept Map

# 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 for arithmetic progression
- Activity No #2 activity for arithmetic progression

## 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 acivity for Harmonic progression
- Activity No #2 acivity for Harmonic progression

## 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 activity for Geometric progression
- Activity No #2 activity for Geometric progression

## 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 activity to show relation between A.M, G.M, H.M
- 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