Progressions

Most of the questions are asked in Public Sector, Banking and Various Management Entrance Exams.

There are 3 types of Progressions

1. Arithmetic Progression

2. Geometric Progression

3. Harmonic  Progression

Arithmetic Progression 

Quantities are said to be in A.P when they increase or decrease by a common difference.

Example-

1.All Natural Numbers are in A.P with Common Difference 1

   i.e- 1, 2,3,4,5.....

2. All Even and Odd Numbers are in A.P having Common Difference 2

   i.e- even numbers 2,4,6,8...

          odd numbers 1,3,5,7,9....

Arithmetic Progression can be represented as 

a, a+d, a+2.d, a+3.d,........ 

where a- first term

           d- common difference

Nth term of Series 

Sum of Series-

 

To find the Arithmetic Mean between any two given quantities is given by 

Examples

Geometric Progression

Quantities are said to be in G.P when they increase or decrease by constant factor, which is called common ratio.

Example

3, 6, 12, 24, ....

2, 6,18, 54, .....

Geometric Progression can be represented as

nth Term of GP is 

Sum of n term of a G.P

To find Geometric Mean between 2 numbers a, b is given by 

Examples

Harmonic Progression

If a,b,c,d are in Arithmetic Progression then 

Harmonic Mean of a and b is 

Example

All the Three Progressions are discussed and examples are solved for each Progression.

                                                              Thank-You!