Find the missing value in the series: 51, 52, 60, 87, 151, _____________, 
492.

To find the missing value in the series: 51, 52, 60, 87, 151, ____, 492, let's first look at the differences between consecutive terms.

1. \( 52 - 51 = 1 \)
2. \( 60 - 52 = 8 \)
3. \( 87 - 60 = 27 \)
4. \( 151 - 87 = 64 \)

These differences follow a pattern: \( 1, 8, 27, 64 \), which are cubes of consecutive integers:
\[
1^3 = 1, \quad 2^3 = 8, \quad 3^3 = 27, \quad 4^3 = 64
\]

Following this pattern, the next difference should be \( 5^3 = 125 \).

So, the next term after 151 would be:
\[
151 + 125 = 276
\]

Let's check if the pattern holds by calculating the difference between 276 and the next given number in the sequence, 492:
\[
492 - 276 = 216 \quad \text{(which is } 6^3\text{, fitting the pattern)}.
\]

Therefore, the missing value in the series is \( \boxed{276} \).

Would you like further details or have any other questions?

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Here are 5 relative questions to expand the concept:
1. What is the general formula for the difference between terms in this series?
2. How can you determine a missing term if the pattern is less obvious?
3. Can cube numbers form any other recognizable sequences?
4. What are the patterns for sequences involving squares instead of cubes?
5. How can this problem be approached if the differences don’t follow a cubic pattern?

**Tip:** When dealing with number sequences, always check for patterns in the differences, as they often reveal a relationship such as squares, cubes, or other mathematical operations.

Find the missing value in the series: 51, 52, 60, 87, 151, _____________, 492.

Learn how to find the missing value in the number series 51, 52, 60, 87, 151, ____, 492. This solution uses the properties of cubic numbers and the differences between terms. Suitable for students in Grades 8-10.

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