Math Problem Statement
10, 100, 200, 310, ?
Solution
The sequence you provided appears to follow a non-linear pattern. Let's analyze it step by step:
- From to : the difference is .
- From to : the difference is .
- From to : the difference is .
The differences between consecutive terms are increasing by 10 each time (90, 100, 110).
If this pattern continues, the next difference should be .
Therefore, the next term in the sequence would be:
So, the next term in the sequence is 430.
Would you like more details or have any questions?
Here are five related questions:
- What type of sequence is this (arithmetic, geometric, etc.)?
- Can you find the -th term formula for this sequence?
- How would the sequence behave after 5 more terms?
- What would happen if the difference between terms increased by a different value (e.g., 20 instead of 10)?
- How does this sequence compare to a quadratic progression?
Tip: When identifying patterns in sequences, look for changes in the differences between terms to detect a linear or non-linear pattern.
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Math Problem Analysis
Mathematical Concepts
Sequences
Arithmetic Progressions
Non-linear Patterns
Formulas
Difference between terms: d_n = d_(n-1) + 10
Theorems
Arithmetic Progression Formula
Pattern Recognition
Suitable Grade Level
Grades 6-8
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