Question

in an AP the sum of three consecutive terms is 27 and their product is 504 find the terms​

Answer 1

Answer:

Step-by-step explanation:

Three terms

a-d,a,a+d

Sum= 27

a-d+a+a+d= 27

3a= 27

a= 9

Now product

a(a^2-d^2)= 504

9(81-d^2)=504

81-d^2=56

D^2=25

D= 5

AP: 4,9,14

Answer 2

Answer:

4, 9, 14

Step-by-step explanation:

Let the three terms be x - d, x & x + d, where x is the second term and d is the common difference.

⇒ Sum of the terms = 27

⇒ x - d + x + x + d = 27

⇒ 3x = 27

⇒ x = 9

Thus the second term is 9.

⇒ Product of terms = 504

⇒ (x - d) x (x + d) = 504

⇒ x(x - d)(x + d) = 504

⇒ x(x² - d²) = 504

⇒ 9(9² - d²) = 504       [∵ x = 9]

⇒ 9(81 - d²) = 504

⇒ 81 - d² = 504 / 9

⇒ 81 - d² = 56

⇒ d² = 81 - 56

⇒ d² = 25

⇒ d = ±5

Thus the common difference is either 5 or -5.

Taking d = 5...,

⇒ x - d = 9 - 5 = 4

⇒ x + d = 9 + 5 = 14

 

Taking d = -5...,

⇒ x - d = 9 - (-5) = 9 + 5 = 14

⇒ x + d = 9 + (-5) = 9 - 5 = 4

 

Thus the terms are 4, 9 and 14.

And the possible APs are 4, 9, 14,... and 14, 9, 4,...