The sum of three consecutive terms that are in A.P. is 27 and their product is 288. Find the three terms.

Solution :

Let the three terms are a - d, a and a + d.

Sum of three consecutive terms = 27

a - d + a + a + d = 27

3a = 27

a = 27/3 = 9

Product of three terms = 288

(a - d) a (a + d) = 288

a(a2 - d2) = 288

9(92 - d2) = 288

(92 - d2) = 288/9

(92 - d2) = 32

- d2 = 32 - 81

- d2 = - 49

d = 7

1st term = a - d = 9 - 7 = 2

2nd term = a = 9

3rd term = a + d = 9 + 7 = 16

Hence the first three terms are 2, 9, 16.