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If a,b,c are in A.P. Prove that b+c,c+a,a+b are also in A.P.?
if a,b,c are in AP then
b-a=c-b
a+c=2b ...........1
now we have to prove that b+c,c+a,a+b are in AP,
let these are in AP then
(a+c)-(b+c)=(a+b)-(a+c)
(a+c)=2b
from eq 1 we have a+c=2b ,RHS=LHS
so these terms are also in AP...
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