I have finished all my homework but I have one problem that I cannot answer. The teacher said that no one could probably answer this. Can someone help?

We have to find the next three numbers in the pattern and explain the rule for the pattern.

8, 27, 64, ________, ________, ________

look at cubes.

d

125, 216, 343. the rule is x^3. 125 = 5^3, 216 = 6^3, 343 = 7^3.

To find the next three numbers in the pattern and explain the rule, we need to first understand the pattern. From the given numbers 8, 27, 64, we can observe that each number is a cube of some integer.

In mathematics, a cube of a number is obtained by multiplying the number by itself twice. For example, 2 cubed (or 2^3) is equal to 2 × 2 × 2 = 8. Similarly, 3 cubed (or 3^3) is equal to 3 × 3 × 3 = 27, and 4 cubed (or 4^3) is equal to 4 × 4 × 4 = 64.

Now, let's use the rule of cubes to find the next three numbers. We need to continue cubing the consecutive integers after 4:

5 cubed (or 5^3) = 5 × 5 × 5 = 125 (the next number)
6 cubed (or 6^3) = 6 × 6 × 6 = 216 (the second next number)
7 cubed (or 7^3) = 7 × 7 × 7 = 343 (the third next number)

So, the next three numbers in the pattern are 125, 216, and 343. The rule for the pattern is that each number in the sequence is obtained by cubing consecutive integers.