Question

The number x, y, z are in an arithmetic sequence. If x-y=k(z-x), find value of k

Answer 1

Answer:

-1/2

Step-by-step explanation:

x,y,z are in arthimetic sequence

then,2y=x+z

x=2y-z........(1)

given,

x-y=k(z-x)

x-y=kz-kx

x+kx=kz+y

x(1+k)=kz+y

(2y-z)(1+k)=kz+y

2y-z+2ky-kz=kz+y

By solving it

y-z=2kz-2ky

y-z=-2k(y-z)

-2k=1

k=-1/2

Hope it is helpful to you....