a,b,c are in AP proove that …
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Poulami Dasgupta 6 years, 8 months ago
Since a, b, c are in AP, the common difference will be same
b—a=c—b
b+b=c+a
2b=c+a
2b—c=a-------(i)
Now to show b+c, c+a,a+b in A.P , the common difference should be same in each case
1st common difference = (c+a)—(b+c)
= c+a—b—c
= a—b
=2b—c—b(from (i))
= b—c
2nd common difference = ( a+b)—(c+a)
= a+b—c—a
=b—c
Since, both the common difference is same , so (b+c), (c+a),(a+b) are in AP
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