Question

7. Inan A.P. sum of three consecutive terms is 27 and their product is 504, find the terms.
(Assume that three consecutive terms in A.P. are
a-d, a, a + d.)​

Answer 1

Step-by-step explanation:

now,

a-d + a + a+d= 27

therefore,

a+a+a= 27

=→ 3a= 27

therefore a= 9.

now,

(a-d)(a)(a+d)= 504

=→ (9-d)(9)(9+d)= 504

=→ (81-9d)(9+d)= 504

=→ 729+81d-81d-9d= 504

=→ 729-9d² =504

=→ 729-504= 9d²

=→ 225= 9d²

=→ 25= d²

therefore

d= 5

now,

the terms are.... a-9= 4. [ans]

a. = 9. [ans]

a+d= 14. [ans]

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