Let A be the first term and D the common difference of A.P.\\\\(T_p=a=A+(p-1)D=(A-D)+pD\\\\) \\\\((1)\\\\)\\\\(T_q=b=A+(q-1)D=(A-D)+qD\\\\) ..\\\\((2)\\\\)\\\\(T_r=c=A+(r-1)D=(A-D)+rD\\\\) ..\\\\((3)\\\\)Here we have got two unknowns A and D which are to be eliminated.We multiply \\\\((1), (2)\\\\) and \\\\((3)\\\\) by \\\\(q-r, r-p\\\\) and \\\\(p-q\\\\) respectively and add:\\\\(a(q-r)+b(r-p)+c(p-q)\\\\)\\\\(=(A-D)[q-r+r-p+p-q]+D[p(q-r)+q(r-p)+r(p-q)]=0\\\\).