if a,b,c are in AP, shoe that b+c,c+a,a+b, are also in AP.
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If a,b,c are in AP
a+c=2b
we need to prove a+b,c+a,b+c are in AP
∴ 2 (a+c) = b + c + a + b
2c + 2a = 2b + c + a
a+c = 2b
∴ proved.
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