The 2nd term in a geometric sequence is -4 and the 5th term is 32

a + ar + a r^2 + a r^3 + a r^4

ar = -4
a r^4 = 32

a = -4/r

(-4/r) r^4 = 32

r^3 = -8
so r = -2
and a = 2

To find the common ratio in a geometric sequence, you can use the formula:

common ratio = (n-th term) / (previous term),

In this case, we are given that the 2nd term is -4 and the 5th term is 32.

To find the common ratio, we can use the following steps:

Step 1: Calculate the difference between the 5th term and the 2nd term.
difference = 32 - (-4) = 36.

Step 2: Calculate the difference between the 2nd term and the 1st term (which we don't know yet).
Since we know the 2nd term (-4), we can use the common ratio formula: -4 = (1st term) / (common ratio).

Step 3: Rearrange the formula to solve for the 1st term:
1st term = -4 * common ratio.

Step 4: Substitute the 1st term into the common ratio formula as (-4 * common ratio) to get:
-4 = (-4 * common ratio) / common ratio.

Step 5: Simplify the equation:
-4 = -4.

Since both sides of the equation are equal, we can conclude that the common ratio is 1.

Therefore, in this geometric sequence, the common ratio is 1.