The sequence of cube numbers is formed by taking each integer and raising it to the power of 3. This gives the sequence:

$1^3, 2^3, 3^3, 4^3, 5^3, \dots$

Which is:

$1, 8, 27, 64, 125, 216, 343, \dots$

a) Finding the nth term rule for the sequence of cube numbers:

The nth term in this sequence can be expressed as:

$a_n = n^3$

Where $n$ is the position of the term in the sequence.

b) Finding the 17th term in this sequence:

To find the 17th term, we substitute $n = 17$ into the formula:

$a_{17} = 17^3 = 17 \times 17 \times 17 = 4913$

Thus, the 17th term in the sequence of cube numbers is 4913.

Would you like more details or have any further questions?

Here are 5 related questions for further exploration:

1. How do you find the nth term for a sequence of square numbers?
2. What is the difference between cube numbers and square numbers?
3. Can you explain how to calculate powers of larger numbers more efficiently?
4. How does the graph of cube numbers look compared to the graph of square numbers?
5. What is the general formula for the sum of the first $n$ cube numbers?

Tip: To quickly calculate cubes of numbers, use the identity $(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$. This can help break down and simplify larger cubes!