Question

3 distinct numbers x y z form an gp in that order and the numbers 7x+5y , 7y+5z , 7z+5x form an ap in that order. The common ratio of gp.
options
-4
-2
10
18

Answer 1

Answer:

The common ratio of the G.P is -4

Step-by-step explanation:

$\text{Given: }$

$\text{x, y, z are in G.P }$

$\text{Let r be the common ratio}$

$\text{Then, }$

$y=xr$ and

$z=xr^2$

Also,

$7x+5y,\;7y+5z,\:7z+5x\text{ are in A.P}$

$\implies(7y+5z)-(7x+5y)=(7z+5x)-(7y+5z)$

$\implies\,2y+5z-7x=2z+5x-7y$

$\implies\,9y+3z-12x=0$

$\implies\,9y+3z=12x$

$\implies\,3y+z=4x$

$\implies\,3(xr)+(xr^2)=4x$

$\implies\,3r+r^2=4$

$\implies\,r^2+3r-4=0$

$\implies\,(r+4)(r-1)=0$

$\implies\,\boxed{r=-4,1}$

Answer 2

Answer:

Hope it will help you ☺️