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प्रश्न
The sum of three consecutive terms that are in A.P. is 27 and their product is 288. Find the three terms
उत्तर
Let the three consecutive terms be a – d, a and a + d
By the given first condition
a – d + a + a + d = 27
3a = 27
a = `27/3` = 9
Again by the second condition
(a – d) (a) (a + d) = 288
a(a2 – d2) = 288
9(81 – d2) = 288 (a = 9)
81 – d2 = `288/9`
81 – d2 = 32
∴ d2 = 81 – 32
= 49
d = `sqrt(49)` = ± 7
When a = 9, d = 7
a + d = 9 + 7 = 16
a = 9
a – d = 9 – 7 = 2
When a = 9, d = – 7
a + d = 9 – 7 = 2
a = 9
a – d = 9 – (–7) = 9 + 7 = 16
The three terms are 2, 9, 16 (or) 16, 9, 2
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