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If a,b,c are in A.P. prove that b+c,c+a,...

If a,b,c are in A.P. prove that `b+c,c+a,a+b ` are also in A.P.

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Since a, b, c, are in A.P.
`rArr a - (a + b + c), b - (a + b+ c), c - (a + b + c ) ` are in A.P.
[subtracting `a + b + c ` from each term]
`rArr - (b + c), - (c + a), - (a + b) ` are in A.P.
`rArr (b + c), (c + a), (a + b)` are in A.P. " " [On dividing each term by - 1]
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