The sequence you've provided is:
$1, 8, 27, 64, \dots$

This sequence represents the cubes of natural numbers. Specifically:

$1 = 1^3, \quad 8 = 2^3, \quad 27 = 3^3, \quad 64 = 4^3, \dots$

Thus, the nth term of the sequence can be written as: $a_n = n^3$

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

For example:

• For $n = 1$, the term is $1^3 = 1$,
• For $n = 2$, the term is $2^3 = 8$,
• For $n = 3$, the term is $3^3 = 27$,
• For $n = 4$, the term is $4^3 = 64$, and so on.

Would you like more detailed steps, or is there any other aspect you'd like to explore?

Related Questions:

1. What is the sum of the first 5 terms of this sequence?
2. How can you represent the sequence in a general formula for any power, such as $n^k$?
3. What is the nth term of a similar sequence: 1, 4, 9, 16, 25...?
4. How do you find the sum of cubes up to a certain term in the sequence?
5. Can the nth term of this sequence be generalized for negative $n$?

Tip:

For sequences involving powers (like cubes or squares), recognizing the pattern of powers can simplify finding the nth term quickly!