Question

In a G.P the product of three consecutive terms is 27 and the sum of the product of two terms taken at a time is 572.Find the three terms.​

Answer 1

Answer:

The three terms are either 2, 3, 9/2 or 9/2, 3, 2.

Step-by-step explanation:

Let three consecutive terms of a GP are a/r, a, ar.

Product of three consecutive terms is 27.

a/r ×r×ar = 27

a^3 = 27

a = 3

The sum of the product of two terms taken at a time is 57/2.

a/r*a+a*ar+a/r*ar = 57/2

a^2/r + a^2r + a^2 = 57/2

Substitute a = 3

3^2/r + 3^2r + 3^2 = 57/2

9/r + 9r + 9 = 57/2

9 + 9r^2 / r= 57/2 - 9

9 + 9r^2 / r = 39/2

18 + 18r^2 = 39r

18r^2 - 39r + 18 = 0

(2r-3) (9r-6) = 0

r = 3/2, 2/3

For a = 3 and r = 3/2 and three terms are 2, 3, 9/2....

For a = 3 and r = 2/3 and three terms are 2, 3, 9/2....

Therefore, the three terms are either 2, 3, 9/2 or 9/2, 3, 2.