Arithmetic Mean

Arithmetic Mean

If a, b, c are in A.P . Then middle term of this A.P is known as arithmetic mean of an A.P.

let b be arithmetic mean in a, b, c .

     b =  (a + c)/2

  1. Single arithmetic mean of  ’n’ positive numbers :

Let us assume ’n’ positive numbers —

a1, a2 , a3, ….. , an.

and A be the arithmetic mean of an A.P.

then 

           A =  (a1 + a2 + a3 + ……. + an)/n.

2. n-Arithmetic means between two numbers

Let

a & b be the two numbers and  A1 ,A2 , A3 , ……, An. are arithmetic means between a & b .

Then

a , A1 ,A2 , A3 , …….. , An , b. will be in A.P.

Now ,

  a = 1st term

  b = (n+2)th term   

     = a + (n + 2 – 1)d

d = (b-a)/(n+1)

then ,

A1 = a + d       = a + (b-a)/(n+1)

A2 = a + 2d.   =  a + 2(b-a)/(n+1)

:

:

:

An = a + nd

      = a + n(b-a)/(n+1)

An =  a + n(b-a)/(n+1)