https://file.aiquickdraw.com/mathbot/file/1726998984409b4h54rmf.jpg

The sequence provided is: 

142, 150, 123, 187, 62, ?

Let's look for a pattern in this sequence:

1. The difference between the first and second terms:  
   \( 150 - 142 = 8 \)

2. The difference between the second and third terms:  
   \( 123 - 150 = -27 \)

3. The difference between the third and fourth terms:  
   \( 187 - 123 = 64 \)

4. The difference between the fourth and fifth terms:  
   \( 62 - 187 = -125 \)

The differences follow a pattern:  
\( 8, -27, 64, -125 \)

This is a sequence of increasing differences that seem to follow powers of numbers:
- \( 2^3 = 8 \)
- \( -3^3 = -27 \)
- \( 4^3 = 64 \)
- \( -5^3 = -125 \)

If we continue this alternating sign pattern using the next cube in the series, the difference should be \( 6^3 = 216 \), but negative:
  
So, the next difference is \( -216 \).

Finally, to find the missing number:
  
\( 62 - 216 = -154 \)

Thus, the missing number is **-154**.

Would you like further clarification or a more detailed breakdown?

Here are 5 related questions to deepen your understanding:
1. How can recognizing patterns in sequences help in solving real-world problems?
2. What are the common types of sequences found in mathematics?
3. Can you identify other examples where the pattern alternates between positive and negative powers?
4. What are the key differences between arithmetic and geometric sequences?
5. How can the concept of exponents and powers assist in identifying sequence patterns?

**Tip:** Always check if differences in a sequence follow powers, factorials, or other mathematical functions, especially when no linear pattern is evident.

Learn how to find the missing number in the sequence 142, 150, 123, 187, 62 by identifying the pattern based on alternating cubes of integers. Step-by-step solution provided for students in Grades 6-8.

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