If a,b,c are in A.P. Prove that b+c,c+a,a+b are also in A.P.?

1.	If a,b,c are in A.P. Prove that b+c,c+a,a+b are also in A.P.?
Answer» b + c, c + a, a + b will be in AP, if(c + a) - (b + c) = (a + b) - (c + a){tex}\\Rightarrow{/tex}\xa0a - b = b - c\xa0{tex}\\Rightarrow{/tex}\xa02b = a + ci.e., a, b, c are in AP.Thus, a, b, c are in AP implies b + c, c + a, a + b are also in AP.Hence proved.

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