The sum of three numbers forming a geometric progression is equal to 56. if we subtract 1,7,21 from these numbers, respectively, then the newly obtained numbers will form an arithmetic progression. Find the common ratio (integral value) of the G.P.

Answer

2

Explanation

`(a)/(r)+a+ar=56`
`((a)/(r)-1)+(ar-21)=2(a-7)`
`implies(a)/(r)+ar-22=2a-14`
`implies(a)/(r)+ar=2a+8`
`impliesa+(a)/(r)+ar=3a+8=56`
`implies3a=48impliesa=16`
Also `16((1)/(r)+1+r)=56`
`(1+r+r^(2))/(r)=(7)/(2)`
`implies2+2r+2r^(2)=7t`
`implies2r^(2)-5r+2=0`
`implies2r^(2)-4r-r+2=0`
`2r(r-2)-1(r-2)=0`
`impliesr=(1)/(2),2`
`because` numbers are `(16)/(2),16,16xx2`