What number completes the pattern: -4, -6, -9, -6, ?, …

Mathematics Questions

What number completes the pattern? note that there is a single algebraic equation (limited to the basic arithmetic operations of addition, subtraction, multiplication, and division) that repeats across all rows.-4 -6 -9 -6 ? 7 4 -4 9 3 2 6 3 -4 8 -6

Short Answer

The sequence alternates between descending and ascending values. By analyzing the patterns, the missing number is determined to be 5, as it follows the pattern of increasing by 5 from the last number in the ascending sequence.

Step-by-Step Solution

Identify the Pattern

To begin solving the sequence, observe the numbers: -4, -6, -9, -6, ?, 7, 4, -4, 9, 3, 2, 6, 3, -4, 8, -6. Notice the alternating structure of the sequence where certain numbers decrease while others increase. Recognizing this will help us understand how to find the missing number.

Analyze Descending and Ascending Orders

Examine the two distinct sequences presented. The first sequence, which is descending, begins at -4 and decreases with a specific pattern of increasing values:

  • -4 to -6 (decrease of 2)
  • -6 to -9 (decrease of 3)

In the second sequence, which ascends from the missing value, observe how the values increase:

  • -6 to 7 (increase of 13)
  • 7 to 4 (decrease of 3)

Determine the Missing Number

Utilizing the insights from the earlier steps, we can now find the missing number. This number should be 2 more than the last ascending number. The last ascending number before the missing value is -6, meaning the missing number will be:

  • -6 + 5 = 5

Thus, the missing number in this consistent pattern is 5.

Related Concepts

Pattern Recognition

The ability to identify regularities and trends within a set of data or numbers that can help deduce or predict further elements in the series

Ascending Sequence

A series of numbers in which each subsequent number is greater than the previous one, showing an upward trend

Descending Sequence

A series of numbers in which each subsequent number is less than the previous one, showcasing a downward trend.

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