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.
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.