Question

if b+c, c+a, a+b are in AP. Prove a, b, c are in AP​

Answer 1

Answer:

If a,b,c are in AP

a+c=2b

we need to prove a+b,c+a,b+c are in AP

∴2(a+c)=b+c+a+b

2c+2a=2b+c+a

a+c=2b

∴proved.

Step-by-step explanation:

Answer 2

Answer:

c+a - (b+c) = c+a-b-c = a-b ----- equation 1

a+b - (c+a) = a+b-c-a = b-c ----- equation 2

Both equations must be equal because the common difference is always same.

a-b = b-c

-(a-b) = -(b-c)

b-a = c-b

Hence, as there common difference is same so they are in AP.

Hence, Proved!!