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.

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

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

Is there a term-to-term rule for the sequence below?

18 , 22 , 26 , 30

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!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Series questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

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 $1^3 = 1$ ?