**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)**

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