Question

In an ap sum of three consecutive terms is 27 and their product is 504 find the terms assume that three consecutive terms in AP are a minus b, a a + b

Answer 1

if I'm not wrong the Answer should be 4,9,14

Answer 2

the given AP is a-b, a, a+b,.....
their product = a(a-b)(a+b) = 504 --- (1)
and a-b+a+a+b = 27
=> 3a = 27
=> a = 9
putting a = 9 in (1)
9(9-b)(9+b) = 504
=> 9 × (9^2 - b^2) = 504
=> 9 × (81 - b^2) = 504
=> 729 - 9b^2 = 504
=> -9b^2 = 504 - 729
=> b = 5

a-b = 9-5 = 4
a+b = 9+5
therefore the three consecutive terms are 4, 9 and 14