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 1010 to 100100: the difference is 10010=90100 - 10 = 90.
  • From 100100 to 200200: the difference is 200100=100200 - 100 = 100.
  • From 200200 to 310310: the difference is 310200=110310 - 200 = 110.

The differences between consecutive terms are increasing by 10 each time (90, 100, 110).

If this pattern continues, the next difference should be 110+10=120110 + 10 = 120.

Therefore, the next term in the sequence would be: 310+120=430310 + 120 = 430

So, the next term in the sequence is 430.

Would you like more details or have any questions?

Here are five related questions:

  1. What type of sequence is this (arithmetic, geometric, etc.)?
  2. Can you find the nn-th term formula for this sequence?
  3. How would the sequence behave after 5 more terms?
  4. What would happen if the difference between terms increased by a different value (e.g., 20 instead of 10)?
  5. 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