Number Series Pattern Explained

The question asks us to identify the pattern in the given number series and find the missing number represented by $(?)$. The series is: 120, 131, 115, 126, 110, (?).

Finding the Series Pattern

Let's analyze the difference between consecutive numbers in the series:

• From 120 to 131: The difference is $131 - 120 = +11$.
• From 131 to 115: The difference is $115 - 131 = -16$.
• From 115 to 126: The difference is $126 - 115 = +11$.
• From 126 to 110: The difference is $110 - 126 = -16$.

We can observe an alternating pattern of operations: add 11, then subtract 16. This pattern repeats.

Calculating the Missing Number

Following the established pattern (+11, -16, +11, -16), the next operation should be adding 11 to the last number in the series.

The last given number is 110. Applying the next step in the pattern:

Missing Number = Last Number + 11

Missing Number = $110 + 11$

Missing Number = $121$.

Conclusion

Therefore, the missing number in the series 120, 131, 115, 126, 110, (?) is 121.