Question

If a,b,c are in A.P., prove that the following is also in A.P.: b+c-a,c+a - b, a+b - c

Answer 1

okk ? I think it will be right

Answer 2

Answer:

Step-by-step explanation:

For AP a,b,c :

Common difference (d) = b-a = c-b

For AP b+c-a, c+a-b, a+b-c :

Common difference (D) = (c+a-b) - (b+c-a) = (a+b-c) - (c+a-b)

Or D= 2(a-b) = 2(b-c)

D= -2(d) = -2(d)

As the common difference is same, therefore it's in AP