Question

The sum of three numbers in GP is 21/2 and their product is 27. What are the numbers?​

Answer 1

Step-by-step explanation:

GIVEN

We are given that in a GP the sum of three terms is 21/2 and their product is 27

TO FIND

We need to find those three terms of that GP

SOLUTION

Let us assume that a/r , a , ar are the three terms of the GP

Product of the three terms = 27

==> a/r × a × ar = 27

==> a^3 = 27

==> a = 3

Sum of three terms = 21/2

==> a/r + a + ar = 21/2

==> a+ ar + ar^2 / r = 21/2

==> a[ 1 + r + r^2] / r = 21/2

==> 1 + r + r^2 / r= 21/2 × 1/3

==> 1 + r + r^2/ r = 7/2

==> 1 + r + r^2 = 7/2r

==> r^2 + 1 - 5/2 r = 0

==> r^2 - 5/2 r + 1 =0

==> 2r^2 - 5r + 2 = 0

==> r = 4

The terms are,

when r = 4

3/4 , 3, 12

Therefore, the terms are 3/4, 3 , 12