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

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.

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