A sequence follows the rule that each term after the first is obtained by multiplying the previous term by a constant k. If the second term is 12 and the fourth term is 72, what is the value of k?
Let's denote the terms of the sequence as a_1, a_2, a_3, etc., where a_n represents the nth term. According to the given information, we have:

a_2 = 12
a_4 = 72

Since each term is obtained by multiplying the previous term by a constant k, we can write the following relationships:

a_2 = a_1 * k
a_3 = a_2 * k
a_4 = a_3 * k

We want to find the value of k. To do this, let's express a_3 and a_4 in terms of a_1 and k:

a_3 = a_2 * k = (a_1 * k) * k = a_1 * k^2
a_4 = a_3 * k = (a_1 * k^2) * k = a_1 * k^3

Now, we can use the given values of a_2 and a_4 to solve for k:

72 = a_1 * k^3
12 = a_1 * k

Divide the first equation by the second equation:

(72 / 12) = (a_1 * k^3) / (a_1 * k)
6 = k^2

Taking the square root of both sides:

k = √6

So, the value of k is √6.