Question

If 192;x;y;3 form a geometric progression, calculate the value of x and y.

Answer 1

3d = 3-192 = -189
d = -63

192;129;66;3

Answer 2

192,x,y,3,.....
t1 ,t2,t3,t4,...
if it is in GP then
(t2/t1)=(t3/t2)=(t4/t3)
then (t2/t1)=x/192.........(1)
(t3/t2)=y/x...........(2)
(t4/t3)=3/y...........(3)
Now (1)=(2)

x/192=y/x
=>192y=x^2.......(4)

Also
(2)=(3)

y/x=3/y

=>3x=y^2.........(5)

from (2)=> (y^2)/3 substitute in (4)

=>192y=((y^2)/3)^2
=>192y=(y^4)/9
=>192*9=y^3
=>1728=y^3

=>y=12 substitute in (5)

=>we get x=48

therfore x=48,y=12
then verify the series
192,48,12,3........

Hence solved.