Math Problem Statement

Solve

Identify the missing number in the sequence: 3, 5, 8, 13, 22, ? Options: (a) 33, (b) 37, (c) 39, (d) 46.

Solution

Let's analyze the sequence presented in the image.

The numbers in the triangles are: 3,5,8,13,22,?3, 5, 8, 13, 22, ?

Step-by-step reasoning:

  1. Calculate the difference between consecutive numbers:

    • 53=25 - 3 = 2
    • 85=38 - 5 = 3
    • 138=513 - 8 = 5
    • 2213=922 - 13 = 9
  2. The differences are: 2,3,5,92, 3, 5, 9.

  3. Notice that these differences seem to follow a pattern related to Fibonacci-like numbers:

    • 2,3,5,9,...2, 3, 5, 9, ... (next difference is 9+5=149 + 5 = 14).
  4. Add this new difference to the last number in the sequence:

    • 22+14=3622 + 14 = 36.

Thus, the missing number is 36, which is not listed in the options.

Note:

If the image options are misaligned, clarify if the correct options were meant to include 36 or let me know if adjustments are needed.

Would you like further clarification or a detailed breakdown? Here are 5 related questions to expand understanding:

  1. Can you explain why the differences grow following a pattern?
  2. How can we generalize this sequence for larger terms?
  3. What are Fibonacci-like sequences, and how are they applied here?
  4. What if the pattern changes? How can we verify it?
  5. Could there be other interpretations for the sequence rule?

Tip: Always check for arithmetic or Fibonacci-like patterns when analyzing sequences!

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Math Problem Analysis

Mathematical Concepts

Number Sequences
Difference Patterns
Fibonacci-like Sequences

Formulas

Difference between consecutive terms
Pattern growth

Theorems

None (based on observed sequence patterns)

Suitable Grade Level

Grades 6-8