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| 1. |
a,b,c are in AP proove that b+c,c+a,a+b are in AP |
| Answer» Since a, b, c are in AP, the common difference will be sameb—a=c—bb+b=c+a2b=c+a2b—c=a-------(i)Now to show b+c, c+a,a+b in A.P , the common difference should be same in each case1st common difference = (c+a)—(b+c) = c+a—b—c = a—b =2b—c—b(from (i)) = b—c2nd common difference = ( a+b)—(c+a) = a+b—c—a =b—cSince, both the common difference is same , so (b+c), (c+a),(a+b) are in AP | |