The product of the first three terms in geometric progression is 8000. If the first term is 4, find the second and third terms

Hi,

Let the first three terms of the GP be 4, 4r, 4r^2 .

According to the problem,  4 x 4r x 4r^2 = 8000

                                   (4r)^3 - (20)^3 = 0

                                   (4r - 20) (16r^2 + 80r + 400) = 0

                                either 4r - 20 = 0      =>  r = 5

                                or,   16r^2 + 80r + 400 = 0             =>         r^2 + 5r + 25 = 0

                                                                                               r = (-5 ± i 5√3)/2

If imaginary value of r is considered then second and third term of the GP will be imaginary also. Hence product of first three terms will also be imaginary, which is not true. Hence acceptable soln is r = 5.

Therefore three terms are 4, 20, 100 .