Video Lecture & Short Notes:Arithmetic Progression

What is a Sequence?

A list of number in some particular order.

Arithmetic Progression

An arithmetic progression is a sequence of numbers such that the difference of any two successive members is a constant

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Features of Arithmetic Progression

  1. The difference is called the common difference of the AP and It is denoted by d
  2. The members are called terms. The first member is called first term
  3. If a1, a2,a3,a4,a5  are the terms in AP then

     d =   a2  -a1  =   a3  – a2.  =   a4 – a3   =    a5 –a­4

  4. We can represent the general form of AP in the form

    a, a+d, a+2d, a+3d, a+4d ………..

    Where a is first term and d is the common difference

  5. If the AP series has last term then it s finite Arithmetic Progression and if the AP series has infinite then it is called the infinite Arithmetic Progression

nth Term of Arithmetic Progression

Consider the following series: a, a + d, a + 2d, a + 3d, …
a = First term                                              a + d = Second term
a + 2d = Third term                                  a + 3d = Fourth term and so on

nth term = a + (n – 1)d

Sum of n terms in Arithmetic Progression

S = (n/2)[2a + (n – 1)d]

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