Let the three numbers of the A.P. be a – d, a, a + d
From the question,
Sum of these numbers = 27
a – d + a + a + d = 27
⇒ 3a = 27
a = 27/3 = 9
Now, product of these numbers = 648
(a – d)(a)(a + d) = 648
a(a2 – d2) = 648
a2 – 648/a = d2
92 – (648/9) = d2
93 – 648 = 9d2
729 – 648 = 9d2
81 = 9d2
d2 = 9
d = 3 or -3
Hence, the terms are 9-3, 9 and 9+3 ⇒ 6, 9, 12 or 12, 9, 6 (for d = -3)