# If #m-1, 3m-2, 5m# is a geometric sequence, then what is the value of #m# ?

##### 1 Answer

There is no Real value of

It is possible to get a geometric sequence of Complex numbers with:

#m = 7/8+-sqrt(15)/8i#

#### Explanation:

If

So in order for

#(3m-2)^2 = (m-1)(5m)#

which expands to:

#9m^2-12m+4 = 5m^2-5m#

Subtract

#4m^2-7m+4 = 0#

The discriminant

#Delta = b^2-4ac#

So in the case of this quadratic in

#Delta = (-7)^2-4(4)(4) = 49-64 = -15#

Since

#m = (-b+-sqrt(b^2-4ac))/(2a)#

#= (-b+-sqrt(Delta))/(2a)#

#= (7+-sqrt(15)i)/8#

#= 7/8+-sqrt(15)/8i#

These values lead to geometric sequences of Complex numbers.