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
- 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)