5,x,y,z.405 are in G.P.Find the value of x,y,z.

Since it is a geometric progression, it has a common ratio:  r

Therefore:  x = 5·r

                   y  =  x·r  =  (5·r)·r  =  5r²

                   z  =  y·r  =  (5r²)·r  =  (5·r·r)·r  =  5r³ 

              405  =   z·r  =  (5r³)·r  =  (5·r·r·r)·r  =  5r⁴

 

Therefore  5·r⁴  =  405     --->     r⁴  =  81     --->     r  =  3     or     r  =  -3

 

There are 4 "steps" going from 5 to 405:  first step going from 5 to x; second step going from x to y; third step going from y to z; and fourth step going from z to 405.  These 4 "steps" give the exponent upon r.