Calculate the First Four Terms of n³ Sequence: Cube Number Series

Q: What's the difference between $ n^2 $ and $ n^3 $ ?

Squares use two factors: $ 3^2 = 3 \times 3 = 9 $Cubes use three factors: $ 3^3 = 3 \times 3 \times 3 = 27 $Remember: cubes always have three identical factors!

Q: Why does $ 1^3 = 1 $ ?

Any power of 1 equals 1! Since $ 1^3 = 1 \times 1 \times 1 = 1 $, the first term is always 1 for any positive integer sequence starting with n = 1.

Q: How do I remember which answer is correct?

Look for the rapid growth pattern! Cube sequences grow much faster than square sequences:Squares: 1, 4, 9, 16 (differences: 3, 5, 7)Cubes: 1, 8, 27, 64 (differences: 7, 19, 37)

Q: Do I always start with n = 1?

For "first four terms" problems, yes! Unless told otherwise, start with n = 1 and work up to n = 4 to find the first four terms of the sequence.

Cube Number Sequences with Integer Terms

For the series $n^3$

Find the first four terms.

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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

00:06 Let's substitute the desired term position in the sequence formula and solve

00:23 This is the first term in the sequence

00:29 We'll use the same method to find the next terms

00:36 Let's substitute the desired term position in the sequence formula and solve

00:45 This is the second term

00:49 Let's substitute the desired term position in the sequence formula and solve

01:00 This is the third term

01:22 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

For the series $n^3$

Find the first four terms.

Step-by-step solution

To solve for the first four terms of the series $n^3$ , we follow these steps:

Step 1: Find the first term by setting $n = 1$ .
Step 2: Use the formula $n^3$ to calculate the cube of 1.
Step 3: Repeat the process for the next three integers: $n = 2, 3,$ and $4$ .

Calculations:

Step 1: For $n = 1$ $1^3 = 1$ Thus, the first term is 1.

Step 2: For $n = 2$ $2^3 = 2 \times 2 \times 2 = 8$ Thus, the second term is 8.

Step 3: For $n = 3$ $3^3 = 3 \times 3 \times 3 = 27$ Thus, the third term is 27.

Step 4: For $n = 4$ $4^3 = 4 \times 4 \times 4 = 64$ Thus, the fourth term is 64.

Therefore, the first four terms of the series $n^3$ are: $1, 8, 27,$ and $64$ .

The correct multiple-choice answer is: $1, 8, 27, 64$

Final Answer

1,8,27,64

Key Points to Remember

Essential concepts to master this topic

Pattern: Cube each positive integer starting from n = 1
Calculation: For n = 3, compute $3^3 = 3 \times 3 \times 3 = 27$
Check: Verify sequence grows rapidly: 1, 8, 27, 64 shows cubing pattern ✓

Common Mistakes

Avoid these frequent errors

Confusing cubes with squares
Don't calculate $n^2$ instead of $n^3$ = getting 1,4,9,16! This gives you square numbers, not cube numbers. Always multiply the number by itself three times for cubes.

Practice Quiz

Test your knowledge with interactive questions

Look at the following set of numbers and determine if there is any property, if so, what is it?

$$ 94,96,98,100,102,104 $$

FAQ

Everything you need to know about this question

What's the difference between $n^2$ and $n^3$ ?

Squares use two factors: $3^2 = 3 \times 3 = 9$
Cubes use three factors: $3^3 = 3 \times 3 \times 3 = 27$

Remember: cubes always have three identical factors!

Why does $1^3 = 1$ ?

Any power of 1 equals 1! Since $1^3 = 1 \times 1 \times 1 = 1$ , the first term is always 1 for any positive integer sequence starting with n = 1.

How do I remember which answer is correct?

Look for the rapid growth pattern! Cube sequences grow much faster than square sequences:

Squares: 1, 4, 9, 16 (differences: 3, 5, 7)
Cubes: 1, 8, 27, 64 (differences: 7, 19, 37)

Do I always start with n = 1?

For "first four terms" problems, yes! Unless told otherwise, start with n = 1 and work up to n = 4 to find the first four terms of the sequence.

What if I make a calculation error?

Double-check each cube calculation step by step. For example: $4^3 = 4 \times 4 = 16$ , then $16 \times 4 = 64$ . Breaking it into steps prevents mistakes!

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Calculate the First Four Terms of n³ Sequence: Cube Number Series

Cube Number Sequences with Integer Terms

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

What's the difference between $n^2$ and $n^3$ ?

Why does $1^3 = 1$ ?

How do I remember which answer is correct?

Do I always start with n = 1?

What if I make a calculation error?

🌟 Unlock Your Math Potential

More Questions

Series / Sequences

Calculate the 10th to 12th Terms of the Sequence: Applying 5n - 3

Find the Third Term in a Sequence with Rule n/2

Identify Even-Numbered Terms: Sequence Using 4n-3 to the Eighth Term

Determine the First Three Terms of the Sequence: 3n + 3

Calculate the First Four Terms of n³ Sequence: Cube Number Series

Cube Number Sequences with Integer Terms

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

What's the difference between n2 n^2 n2 and n3 n^3 n3?

Why does 13=1 1^3 = 1 13=1?

How do I remember which answer is correct?

Do I always start with n = 1?

What if I make a calculation error?

🌟 Unlock Your Math Potential

More Questions

Series / Sequences

Calculate the 10th to 12th Terms of the Sequence: Applying 5n - 3

Find the Third Term in a Sequence with Rule n/2

Identify Even-Numbered Terms: Sequence Using 4n-3 to the Eighth Term

Determine the First Three Terms of the Sequence: 3n + 3

What's the difference between $n^2$ and $n^3$ ?

Why does $1^3 = 1$ ?