What is the common ratio of the geometric sequence whose first term is 27 and fourth term is 64?

The common ratio of the geometric sequence is 4/3.

Here's how we can determine that, based on the information provided:

We're given that the first term of the geometric sequence is 27 and the fourth term is 64. In a geometric sequence, each term is multiplied by a constant value (the common ratio) to obtain the next term.

We can represent this sequence visually as follows:

Term Number	Term Value
1	27
2	27 * r
3	27 r r
4	27 r r * r = 64

Where 'r' is the common ratio.

This visual representation leads us to the equation 27 r r * r = 64, which can be simplified to 27r³ = 64.

To solve for 'r', we can follow these steps:

1. Divide both sides by 27: r³ = 64/27
2. Take the cube root of both sides: r = ∛(64/27)
3. Simplify: r = 4/3

Therefore, the common ratio of the geometric sequence is 4/3.