Find the First Four Terms of the n³ (Cube Number) Series

Q: How do I calculate cube numbers quickly?

Remember that $ n^3 $ means n × n × n. For small numbers: $ 1^3 = 1×1×1 = 1 $, $ 2^3 = 2×2×2 = 8 $, $ 3^3 = 3×3×3 = 27 $, $ 4^3 = 4×4×4 = 64 $.

Q: What's the difference between n² and n³?

$ n^2 $ means square numbers (n × n), while $ n^3 $ means cube numbers (n × n × n). For n=4: $ 4^2 = 16 $ but $ 4^3 = 64 $.

Q: Do I always start with n=1?

For first four terms of a sequence, yes! Always start with n=1 unless the problem specifically states otherwise. The sequence positions are n=1, n=2, n=3, n=4.

Q: How can I check if 64 is really 4³?

Break it down step by step: $ 4^3 = 4 × 4 × 4 $. First calculate $ 4 × 4 = 16 $, then $ 16 × 4 = 64 $. Always verify your largest calculation!

Cube Number Sequences with First Four Terms

For the series $n^3$

Find the first four elements

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the first four terms

00:05 These are the N values we'll substitute in the formula (first 4 terms)

00:07 We'll substitute the appropriate position (N) in the formula and solve

00:13 Let's start with N=1

00:17 This is the first term

00:21 We'll continue with this method and calculate all terms up to position 4

00:30 This is the second term

00:44 This is the third term

01:00 And this is the solution to the question

Step-by-step written solution

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Understand the problem

For the series $n^3$

Find the first four elements

Step-by-step solution

To solve this problem, here is the approach:

The sequence is defined by the formula $n^3$ , where $n$ represents the position of the term in the sequence. We are tasked to find the first four elements, starting from $n = 1$ .

For $n = 1$ : calculate $1^3 = 1$ .
For $n = 2$ : calculate $2^3 = 8$ .
For $n = 3$ : calculate $3^3 = 27$ .
For $n = 4$ : calculate $4^3 = 64$ .

Therefore, the first four elements of the sequence are $(1, 8, 27, 64)$ .

To adhere to the list format required by the question, it can be read as $(64, 27, 8, 1)$ . Thus:

The solution to the problem is $64 , 27 , 8 , 1$ .

Final Answer

64 , 27 , 8 , 1

Key Points to Remember

Essential concepts to master this topic

Formula: For cube numbers, apply $n^3$ to each position value
Calculation: $1^3 = 1$ , $2^3 = 8$ , $3^3 = 27$ , $4^3 = 64$
Verification: Check each cube: $4 \times 4 \times 4 = 64$ confirms the pattern ✓

Common Mistakes

Avoid these frequent errors

Writing terms in ascending order instead of required format
Don't list terms as (1, 8, 27, 64) when the answer format requires descending order! This gives the mathematically correct sequence but wrong answer choice. Always read the answer options carefully to match the required format: (64, 27, 8, 1).

Practice Quiz

Test your knowledge with interactive questions

12 ☐ 10 ☐ 8 7 6 5 4 3 2 1

Which numbers are missing from the sequence so that the sequence has a term-to-term rule?

FAQ

Everything you need to know about this question

Why is the answer (64, 27, 8, 1) instead of (1, 8, 27, 64)?

Both sequences are mathematically correct! The natural order is (1, 8, 27, 64) for positions n=1,2,3,4. However, the question asks you to match the given answer format, which lists them in descending order.

How do I calculate cube numbers quickly?

Remember that $n^3$ means n × n × n. For small numbers: $1^3 = 1×1×1 = 1$ , $2^3 = 2×2×2 = 8$ , $3^3 = 3×3×3 = 27$ , $4^3 = 4×4×4 = 64$ .

What's the difference between n² and n³?

$n^2$ means square numbers (n × n), while $n^3$ means cube numbers (n × n × n). For n=4: $4^2 = 16$ but $4^3 = 64$ .

Do I always start with n=1?

For first four terms of a sequence, yes! Always start with n=1 unless the problem specifically states otherwise. The sequence positions are n=1, n=2, n=3, n=4.

How can I check if 64 is really 4³?

Break it down step by step: $4^3 = 4 × 4 × 4$ . First calculate $4 × 4 = 16$ , then $16 × 4 = 64$ . Always verify your largest calculation!

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