Arithmetic Progressions Class 10 PPT

 Page 1


Arithmetic 
Progression
Page 2


Arithmetic 
Progression
Sequence:   A list of numbers 
having specific relation 
between the consecutive 
terms is generally called a 
sequence.
e.g. 1, 3, 5, 7,……… (next term 
to a term is obtained by 
adding 2 with it)
   & 2, 6, 18, 54,…….( next term 
to a term is obtained by 
multiplying 3 with it) 
Page 3


Arithmetic 
Progression
Sequence:   A list of numbers 
having specific relation 
between the consecutive 
terms is generally called a 
sequence.
e.g. 1, 3, 5, 7,……… (next term 
to a term is obtained by 
adding 2 with it)
   & 2, 6, 18, 54,…….( next term 
to a term is obtained by 
multiplying 3 with it) 
Arithmetic Progression: If various terms of a 
sequence are formed by adding a fixed 
number to the previous term or the 
difference between two successive 
terms is a fixed number, then the sequence 
is called AP.
e.g.1) 2, 4, 6, 8, ……… the sequence of even 
numbers is an example of AP
  2) 5, 10, 15, 20, 25…..
 In this each term is obtained by adding 5 to 
the preceding term except first term.
 
Page 4


Arithmetic 
Progression
Sequence:   A list of numbers 
having specific relation 
between the consecutive 
terms is generally called a 
sequence.
e.g. 1, 3, 5, 7,……… (next term 
to a term is obtained by 
adding 2 with it)
   & 2, 6, 18, 54,…….( next term 
to a term is obtained by 
multiplying 3 with it) 
Arithmetic Progression: If various terms of a 
sequence are formed by adding a fixed 
number to the previous term or the 
difference between two successive 
terms is a fixed number, then the sequence 
is called AP.
e.g.1) 2, 4, 6, 8, ……… the sequence of even 
numbers is an example of AP
  2) 5, 10, 15, 20, 25…..
 In this each term is obtained by adding 5 to 
the preceding term except first term.
 
      Illustrative example for A.P.
               =d,where d=1
         
           
            
            a          a+d       a+2d      a+3d………………
Page 5


Arithmetic 
Progression
Sequence:   A list of numbers 
having specific relation 
between the consecutive 
terms is generally called a 
sequence.
e.g. 1, 3, 5, 7,……… (next term 
to a term is obtained by 
adding 2 with it)
   & 2, 6, 18, 54,…….( next term 
to a term is obtained by 
multiplying 3 with it) 
Arithmetic Progression: If various terms of a 
sequence are formed by adding a fixed 
number to the previous term or the 
difference between two successive 
terms is a fixed number, then the sequence 
is called AP.
e.g.1) 2, 4, 6, 8, ……… the sequence of even 
numbers is an example of AP
  2) 5, 10, 15, 20, 25…..
 In this each term is obtained by adding 5 to 
the preceding term except first term.
 
      Illustrative example for A.P.
               =d,where d=1
         
           
            
            a          a+d       a+2d      a+3d………………
The general form of an Arithmetic Progression 
is  
a , a +d , a + 2d , a + 3d ………………, a + (n-
1)d
Where  ‘a’  is first term  and
 ‘d’ is called common difference.