Question

What is the common ratio for the geometric sequence?

Answer 1

The common ratio is -1/4.

Answer 2

Note this pattern:  Mult. 24 by (-1/4) produces -6.
                              Mult -6 by (-1/4) produces 6/4 = 3/2
                             Mult. 3/2 by (-1/4) produces 3/8

Looks as though you copied the problem down incorrectly.  You wrote 32 for 3/2 and -38 for -3/8.

The common ratio is -1/4.