Short Answer 
The missing number in the sequence is determined through analysis of both the sequence patterns and the differences between successive terms. By following observed changes and estimating potential shifts, the missing number is found to be 6, completing the sequence.
Step 1: Analyze the Sequence
To determine the missing number in the sequence, start by looking closely at the pattern formed by the numbers. The given sequence is 6, -5, -6, 5, -4, 3, 2, -6, 6, 6, 9, 4, -9, ?, 6, 3. Break it down into smaller segments to spot any recurring patterns or cycles.
- First segment: 6, -5, -6
- Second segment: 5, -4, 3
- Third segment: 2, -6, 6
- Fourth segment: 6, 9, 4
- Next term: -9, followed by the missing term, then 6, and 3
Step 2: Identify Numerical Patterns
Next, look for a more numerical approach by assessing the differences between successive terms in the sequence. For example, analyze how the numbers transition from one to another considering their signs and values. Understanding these differences will help in predicting the missing term.
- 6 to -5: -11
- -5 to -6: -1
- -6 to 5: +11
- 5 to -4: -9
- -4 to 3: +7
- 3 to 2: -1
- 2 to -6: -8
- -6 to 6: +12
- 6 to 6: +0
- 6 to 9: +3
- 9 to 4: -5
- 4 to -9: -13
Step 3: Determine the Missing Number
Now that you have derived a sequence of differences, you can make an educated guess about the unknown number. Since the pattern shows a significant drop when moving from -9, use the observed alterations to estimate that the next number follows a similar reset or jump to maintain pattern consistency.
- Given the previous adjustment between -9 and the expected number might follow a larger change, estimate it could swing back toward a positive shift.
- Following the pattern logic: -9 + 15 = 6.
- The expected missing number therefore should be 6, completing the sequence as: 6, -5, -6, 5, -4, 3, 2, -6, 6, 6, 9, 4, -9, 6, 6, 3.