n cubed  write 3 terms in these sequences with an nth term

If the nth term of a sequence is given by \( n^3 \), we can generate the terms by substituting values for \( n \). Here, I'll calculate the first three terms of the sequence where each term is the cube of \( n \).

### Calculation of the First Three Terms:

1. **For \( n = 1 \):**
   \[
   a_1 = 1^3 = 1
   \]

2. **For \( n = 2 \):**
   \[
   a_2 = 2^3 = 8
   \]

3. **For \( n = 3 \):**
   \[
   a_3 = 3^3 = 27
   \]

### First Three Terms of the Sequence
The first three terms in this sequence are:
\[
1, 8, 27
\]

This sequence, defined by \( n^3 \), grows quickly as \( n \) increases.

Would you like further details on this sequence or have any other questions?

Here are five related questions to explore:
1. What would the 4th term of this sequence be?
2. How does the sequence defined by \( n^3 \) differ from the sequence defined by \( n^2 \)?
3. What pattern do you notice in the differences between consecutive terms of this sequence?
4. How can we express the sum of the first three terms of the sequence?
5. How does \( n^3 \) relate to the volume of a cube with side length \( n \)?

**Tip:** Sequences defined by powers of \( n \), like \( n^2 \) or \( n^3 \), grow faster than linear sequences, providing a good way to explore exponential growth.

n cubed write 3 terms in these sequences with an nth term

Discover the first three terms of a sequence defined by the nth term formula n^3. This solution involves basic algebra and cubic functions, providing a foundation in sequences and powers. Ideal for students in Grades 7-9 exploring exponential growth in sequences.

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