Question

6. If a, b, c are in A.P. show that
+
b+c-a,c + a-b, a + b -e are in also in A.P.
​

Answer 1

If these terms are in AP:

2*middle term = sum of extremes

2b = a + c

Therefore, if (b + c - a), (a + c - b), (a + b - c) are in AP:

=> 2*middle term = sum of extreme,is true

=> 2(a + c - b) = (b + c - a)+(a + b - c) is true

=> 2(2b - b) = 2b is true

=> 2(b) = 2b is true

=> 2b = 2b, which is always true for b € R.

Hence, (b + c - a), (a + c - b), (a + b - c) are in AP: