Math Problem Statement
Find the missing value in the series: 51, 52, 60, 87, 151, _____________, 492.
Solution
To find the missing value in the series: 51, 52, 60, 87, 151, ____, 492, let's first look at the differences between consecutive terms.
These differences follow a pattern: , which are cubes of consecutive integers:
Following this pattern, the next difference should be .
So, the next term after 151 would be:
Let's check if the pattern holds by calculating the difference between 276 and the next given number in the sequence, 492:
Therefore, the missing value in the series is .
Would you like further details or have any other questions?
Here are 5 relative questions to expand the concept:
- What is the general formula for the difference between terms in this series?
- How can you determine a missing term if the pattern is less obvious?
- Can cube numbers form any other recognizable sequences?
- What are the patterns for sequences involving squares instead of cubes?
- 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.
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Math Problem Analysis
Mathematical Concepts
Number Sequences
Cubic Numbers
Patterns in Differences
Formulas
nth Term Difference Formula: d_n = n^3
Term Calculation: a_n = a_(n-1) + d_n
Theorems
Properties of Cubic Numbers
Suitable Grade Level
Grades 8-10
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