Question

Three numbers are in A.P. If the sum of these numbers are 27 and the product is 648, find the numbers.

• A. 6
• B. 8
• C. 9
• D. 12

Answer 1

Answer: (A), (C), (D)

The correct options are
A 6
C 9
D 12

Let the three numbers be $a-d,a,a+d$
$a-d+a+a+d=273a=27a=9$
$(a-d)\left(a\right)(a+d)=648$
$a(a^2-d^2)=648$
$9(9^2-d^2)=648$
$9^2-d^2=72$
$d^2=81-72$
$d^2=9$
$d=3$
$\therefore$ The numbers are 6 , 9 , 12.