If a b c are in ap then prove that b+c , c+a , a+b are in ap

dear student, a,b,c in A.P.so b-a=c-bor, 2b= a+c ......................(i)hence (b+c)+(a+b)=2b+a+c=a+c+a+c               (from  (i))=2a+2c=2(a+c)so we can say b+c,c+a, a+b are in A.P.( since 1st +3rd=2*2nd term hold in A.P.)Regards,

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a,b,c are in a.p then subtract a,b,c from a+b+c. ans :- a+b+c-a , a+b+c-b , a+b+c-c. =b+c , c+a , a+b. h .p
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a , b , c are in ap So , 2b = a+c For b+c , c+a , a+b to be in ap u need to show that here also 2b= a+c 2(a+c) = b+c+a+b a+c = 2b Done..... Hope u understood , and 2b= a+c is like an identity , u can call it in ap !
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