https://file.aiquickdraw.com/mathbot/file/173589321406800hvmb1a.jpg

tell me the next number of the next 3 sequences     

Let’s analyze each sequence to determine the pattern and find the next number.

---

### (a) \( 1, 8, 27, \dots \)
This sequence is made up of cubes of integers:
\[
1^3 = 1,\; 2^3 = 8,\; 3^3 = 27,\; \dots
\]
The next number is \( 4^3 = 64 \).

---

### (b) \( 1, 2, 4, 7, 11, \dots \)
Here, the differences between consecutive terms are:
\[
2 - 1 = 1,\; 4 - 2 = 2,\; 7 - 4 = 3,\; 11 - 7 = 4
\]
The differences increase by 1 each time. So, the next difference is \( 5 \), and the next term is:
\[
11 + 5 = 16
\]

---

### (c) \( 1, 4, 9, 25, \dots \)
This sequence is made up of squares of integers:
\[
1^2 = 1,\; 2^2 = 4,\; 3^2 = 9,\; 5^2 = 25
\]
Notice the pattern skips \( 4^2 \). The next number is \( 6^2 = 36 \).

---

### Final Answers:
- **(a):** \( 64 \)
- **(b):** \( 16 \)
- **(c):** \( 36 \)

---

Would you like further details or explanations?  
Here are 5 related questions for practice:  
1. What is the 10th term of the sequence \( 1, 8, 27, \dots \)?  
2. Find the sum of the first 5 terms of \( 1, 2, 4, 7, \dots \).  
3. What would the 7th term of \( 1, 4, 9, 25, \dots \) be?  
4. How can you identify a cubic sequence quickly?  
5. Derive a formula for the \( n \)-th term of \( 1, 2, 4, 7, 11, \dots \).  

**Tip:** Always check the differences between terms or powers of integers to uncover hidden patterns!

Tell me the next number of the next 3 sequences

Learn how to find the next numbers in these sequences: cubes (1, 8, 27, ...), arithmetic progression (1, 2, 4, 7, ...), and squares (1, 4, 9, 25, ...). Detailed solutions provided for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation