Question

The sum of three numbers in GP is 30/10 and their product is 1. Find the numbers

Answer 1

Let a1,a2,a3 be part of a G.P

==> a1 + a2 + a3 = 13/12.... (1)

==> a1*a2*a3 = -1............(2)

But:

a1 = a1

a2= a1*r

a3 = a1*r^2

==> a1+ a2 + a3 = a1 + a1*r + a1*r^2

==> a1 + a1r + a1r^2 = 13/12........(1)

Also:

a1*a2*a3 = -1

==> a1*a1*r *a1^r^2 = a1^3 * r^3 = (a1*r)^3

==> (a1*r)^3 = -1

==> a1*r = -1

==> a1= -1/r........(2)