Math Problem Statement

  1. 100, 98, 96, 94, ___

  2. 12, 13, 15, 18, 22, ___

  3. 7, 20, 47, 94, 167, ___

  4. 1, 4, 2, 8, 6, 24, 22, ___

  5. 11, 23, 48, 99, ___

  6. 6, 13, 27, 55, 111, ___

  7. 8, -24, 72, -216, 648, -1994, ___

  8. 5, 27, 137, 687, 3437, ___

  9. 34, 7, 37, 14, 40, 28, ___

Solution

Here are the solutions for each sequence:

  1. 100, 98, 96, 94, ___
    This sequence decreases by 2.
    Next number: 92.

  2. 12, 13, 15, 18, 22, ___
    The differences are 1, 2, 3, 4 (increasing by 1 each time).
    Next difference: 5.
    Next number: 27.

  3. 7, 20, 47, 94, 167, ___
    The pattern is that each term can be expressed as n×2+1n \times 2 + 1:

    • 7×2+6=207 \times 2 + 6 = 20
    • 20×2+7=4720 \times 2 + 7 = 47
    • 47×2+0=9447 \times 2 + 0 = 94
    • 94×221=16794 \times 2 - 21 = 167
      Next number: 274.
  4. 1, 4, 2, 8, 6, 24, 22, ___
    The pattern alternates:

    • Multiply by 4 and

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Math Problem Analysis

Mathematical Concepts

Sequences
Patterns
Arithmetic Progression
Geometric Progression

Formulas

Arithmetic sequence formula
Geometric sequence formula

Theorems

Principle of mathematical induction

Suitable Grade Level

Grades 6-9