Question

If a, b, c are in A.P. Prove that b+c,c+a,a+b is in A.P.​

Answer 1

Answer:

As a, b, c are in AP, we can say that 2b = a + c. a, b, c are in AP. If we add b to all these terms, the resulting terms should also b in AP because the terms would still have the same common difference.

Step-by-step explanation:

Answer 2

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.