Let x-2, 2v3 , x-3 be the first 3 terms of a geometric sequence. Find...

Question

Let
x-2, 2√3 , x-3
be the first 3 terms of a geometric sequence. Find the value of x (the quadratic equation can be solved by factoring).

Answer 1

If the sequence is geometric, then 2√3/(x-2) = (x-3)/(2√3)

 

Cross multiply to get (x-3)(x-2) = 12

 

                              x²-5x-6 = 0

 

                              (x-6)(x+1) = 0

 

                              x =6 or -1