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**In AP form 2nd term - 1st term = 3rd term - 2nd term**

**b²-a² = c²-b²**

**b²+b² = c²+a²**

**2b² = c²+a²**

**Add**

**2ab+2ac+2bc on both sides**

**2b²+2ab+2ac+2bc = a²+c²+**

**ac+ac+bc+bc+ab+ab**

**2b²+**

**2ab+2ac+2bc = ac+bc+a²+ab+bc+c²+ab+ac**

**2b²+2ab+2ca+2cb = ca+cb+a²+ab+cb+c²+ab+ac**

**2(ba+b²+ca+cb) = (ca+cb+a²+ab) + (cb+c²+ab+ac)**

**2((ba+b²)+(ca+cb)) = ((ca+cb)+(a²+ab)) + ((cb+c²)+(ab+ac))**

**2(b(a+b)+c(a+b)) = (c(a+b)+a(a+b)) + (c(b+c)+a(b+c))**

**2(b+c)(a+b) = (c+a)(a+b) + (c+a)(b+c)**

**Divide whole by (a+b)(b+c)(c+a)**

**'**

**2nd term - 1st term = 3rd term - 2nd term**

**Thus**

**are in AP**