Question

the product of three numbers which are in GP is 216.When 2,1 are added respectively to the second and third numbers the resulting numbers are in AP .Find the numbers

Answer 1

let three number are a/r , a and ar
now
a^3=216
a=6
hence numbers are 6/r, 6 , 6r

again question ask

6/r, (6+2), (6r+1) are in AP
so common difference =constant
8-6/r=6r+1-8
15=6r+6/r
15r=6r^2+6
6r^2-15r+6=0
use quadratic formula
r=2, 1/2

hence numbers are 3,6,12
or 12,6,3

Answer 2

Step-by-step explanation:

Refer to the attachment