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.