Question

if abc are in ap a+k b+k c+k are also in ap

Answer 1

Since a, b, and c are in AP

2b = a + c .....(i)

Now, on adding k to the numbers a, b, and c :-

The new no.s are = (a + k), (b + k), and (c + k)

For them to be in AP :-

(c + k) - (b + k) = (b + k) - (a + k)

c + k - b - k = b + k - a - k

c - b = b - a

a + c = 2b

{which is true from the equation (i)}

Hence, the no.s (a+k), (b+k), (c+k) are also in AP