Question

x, y, z is a geometric sequence with common ratio r and \[x \neq y\] .
if x, 2y, 3z is an arithmetic sequence, find r.

Answer 1

is that the whole question?

Answer 2

yes... what's r in the geometric sequence..

Answer 3

y/x ?

Answer 4

I think \[r=\lim_{n \rightarrow \infty}x _{n}/y _{n}\]

Answer 5

so, 1/3?

Answer 6

yeah.. @UnkleRhaukus .... good one...

Answer 7

\[3\approx\infty\]

Answer 8

are you sure this is the answer?

Answer 9

no

Answer 10

i don't know, but i see it this way:
y=rx,z=r^2x
so: 2y-x=q or 2rx-x=q
also: 3r^2x-x=2q
substituting value for q in the 2º equation:
3r^2x-x=4rx-2x
or: r^2-4/3r-1=0
and solve for r

Answer 11

@dpaInc

Answer 12

is the answer 1/3 in question?

Answer 13

no

Answer 14

i have no idea how he got 1/3

Answer 15

y=xr, z=yr=xr^2
3z - 2y = 2y - x

Answer 16

substitute y an z into that last equation..

Answer 17

oh, right, i made a mistake....

Answer 18

you were getting it though....

Answer 19

...