Arithmetic Progression-Concept And Formula-Quant

Readers ,our today topic isProgression(series)


First of all 
Progression is nothing but series, in which numbers are arranged in some pattern.


Progression  has 3 types
1)Arithmetic Progression
2)Geometric Progression
3)Harmonic Progression

 

We start with  Arithmetic Progression

Define :  
If Difference of any two consecutive number in the series  is called Arithmetic Progression
Series is a,a+d,a+2d,......a+(n-1)d


         a=first term in the series
         d=difference of consecutive number

Ex.2,5,8,11.....

Formulas:

->If we want to find nth term in this progression , formula is tn=a+(n-1)d
here
      tn=nth term in the series
      a=first term in the series
      d=difference of consecutive number

->If we want to find the Summation of all number of series, then formula is 
      Sn=n/2[2a+(n-1)d]
       
      where,
      Sn=Summation Of all number in the series
      a=first term in the series
      d=difference of consecutive number 
      n=total member in the series

->If we know the first term and last term in this series then Summation Formula is easy
that is  Sn=n(a+l)/2
          
          where,

         Sn=Summation Of all number in the series 
       a=first term in the series
        l=last number in the series
        n=total member in the series
      

Geometric Progression

Define :
If ratio of any two consecutive number in the series  is called Arithmetic Progression
Series is a, a*r, a(r^2), a(r^3),a(r^4),a(r^5).....,a(r^n)

            a=first term in the series
            r=ratio of two consecutive number


Formulas:
->If we want to find nth term in this progression , formula is tn=a*(r^ n-1)
here
      tn=nth term in the series

      a=first term in the series
      r=ratio of two consecutive number

->If we want to find the Summation of all number of series, then formula is 
      Sn=a(1- r^n)/(1-r)    if r<1
       Sn=a(r^n -1 )/(r-1)    if r>1
   
      where,
       Sn=Summation Of all number in the series

       a=first term in the series
        r=ratio of two consecutive number 

        n=total member(number) in the series

->In this series if infinite number is available
   then Summation is
          
       Sn=a/(1-r) where -1<r<1

       

Harmonic Progression

Define :
If numbers' reciprocal is in the Arithmetic Progression, then series of number is called Harmonic Progression

Series is 1/a , 1/(a+d) , 1/(a+2d) , 1/(a+3d),........

Formulas:
->To find the nth term of this series
you should find nth term of corresponding arithmetic progression and then reciprocal of that. 

if series is 1/2 , 1/4 , 1/6 .... then 

to find n th term first we find nth term of 2,4,6....
then reciprocal of it is nth term of Harmonic Progression.

I hope this post will help to understand the topic of Progression
Our next topic will be on Median 
thank U.