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3rd

Step-by-step explanation:

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We want to find the explicit rule for the given geometric sequence. We will get the explicit rule:

Remember that in a geometric sequence, each term is given by a constant multiplying the previous term.

For the second and third terms we have:

4 = k*6

k = 4/6 = 0.6... and so on.

So we know that:

k = 4/6 = 2/3.

Now that we know this value, we can write the recursive rule as:

This means that the n-th term is (2/3) times the previous one.

The explicit rule will be just:

This just gives us the value of the n-th term in the sequence as a function of k, n, and the first term on the sequence, A₁.

If you want to learn more about geometric sequences, you can read:

link