Question

If a b c are in AP prove a+k,b+k and c+k are in AP

Answer 1

Hope it may help you...

Answer 2

We know, 2 × middle term = sum of remaining two.

So,

➡ 2 × b = a + c

➡ 2b = a + c -------: ( 1 )

If b + c , c + a , a + b are also in A.P.

2 × ( c + a ) = b + a + b + c is true

Or, 2 × ( c + a ) = c + a + b + b is true

Or, 2 × ( c + a ) = c + a + 2b is true

Or, 2 × ( 2b ) = 2b + 2b is true

Or, 4b = 4b is true

0 = 0

Hence, both are equal. It means that b + c , c + a , a + b are in A.P.