Math Problem Statement

2,6,?, 30, -270

Solution

This sequence appears to follow a multiplicative pattern. Let's analyze it step by step:

  1. The first number is 2.
  2. The second number is 6, which is 2×3=62 \times 3 = 6.
  3. We are missing the third number (denote it by ??).
  4. The fourth number is 30, which is 6×5=306 \times 5 = 30.
  5. The fifth number is -270, which is 30×(9)=27030 \times (-9) = -270.

It seems that the pattern involves multiplying by increasing odd integers (3, 5, -9). So, to find the missing number, we can multiply the second number (6) by the next odd integer, which would be 1:

6×1=66 \times 1 = 6

Thus, the sequence should be:

2,6,6,30,2702, 6, 6, 30, -270

The missing number is 6.

Would you like a more detailed explanation or have any questions?

Here are five related questions:

  1. What are the next two terms in the sequence if the pattern continues?
  2. Can you identify another sequence with a similar alternating multiplication pattern?
  3. How would the sequence change if we multiplied by even numbers instead of odd ones?
  4. What is the general term formula for a sequence that follows a multiplicative pattern?
  5. Can you create a sequence using addition instead of multiplication?

Tip: When working with sequences, check for both arithmetic (addition/subtraction) and geometric (multiplication/division) patterns.

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Math Problem Analysis

Mathematical Concepts

Sequences
Patterns
Multiplication

Formulas

Next term in sequence = Previous term * Odd Integer (increasing pattern)

Theorems

None explicitly involved; pattern recognition and multiplication

Suitable Grade Level

Grades 6-8