Question

in an AP sum of three consective term is 27 and their product is 504 find the terms ( three consecutive term in AP are a-d,a,a+d)
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Answer 1

Step-by-step explanation:

∵ There sum is 27

∴ a - d + a + a + d = 27

$∴a = \frac{27}{3}$

∴ a = 9

∵ their product is 504

∴ (a-d) (a) (a+d) = 504

∴ (a-d) (a+d) (a) = 504

∴ (a²-d²) × a = 504

∴ (9²-d²) × 9 = 504

$∴ (81-d²) = \frac{504}{9}$

∴ 81 - d² = 56

∴ 81 - 56 = d²

∴ 25 = d²

∴ d = 5 --------(taking square root)

∴ a - d = 9 - 5 = 4

∴ a = 9

∴ a + d = 9 + 5 = 14

Those three terms are 4,9,14.

Answer 2

Let the consecutive terms are a - d, a, a + d.

Their sum = 27

⇒ (a - d) + a + (a + d) = 27

⇒ 3a = 27       ⇒ a = 27/3 = 9

Their product = 504

⇒ (a - d)(a)(a + d) = 504

⇒ (9 - d)(9)(9 + d) = 504    {a=9}

⇒ (9 - d)(9 + d) = 504/9

⇒ 9² - d² = 56    ⇒ 81 - 56 = d²

⇒ 25 = d²             ⇒ ± 5 = d   

∴ terms are 9 - 5, 9, 9 + 5 or 9 - (-5), 9, 9 + (-5)

⇒ 4, 9, 14   or 14, 9 , 4