To Find: The three numbers which are in AP.

Given: Sum and product of three numbers are 27 and 648 respectively.

Let required number be (a - d), (a), (a + d). Then,

(a - d) + a + (a + d) = 27 3a = 27 a = 9

Thus, the numbers are (9 - d), 9 and (9 + d).

But their product is 648.

(9 - d) × 9(9 + d)= 648

(9 - d)(9 + d)= 72

81 – d² = 72 d² = 9 d =3

When d=3 numbers are 6, 9, 12

When d= (3) numbers are 12, 9, 6

So, Numbers are 6, 9, 12 or 12, 9, 6.