A geometric sequence of positive integers is formed for which the first term is 3 and the fourth term is 192. What is the third term of the sequence?
To find the third term of the sequence, I need to know the common ratio that multiplies each term to get the next one. I can use the fact that the first term is 3 and the fourth term is 192 to find the common ratio. If I call the common ratio r, then I have the equation 3r^3 = 192. To solve for r, I can divide both sides by 3 and get r^3 = 64. Taking the cube root of both sides, I get r = 4. This means that the sequence is 3, 3 * 4, 3 * 4^2, 3 * 4^3, ... The third term is 3 * 4^2, which is 3 * 16, which is 48.

