120 121 117 126 110 ?

Options

A. 135
B. 145
C. 140
D. 175

Answer

To solve the series: 120, 121, 117, 126, 110, ?, we need to identify the pattern in the differences between the numbers.

### Step-by-Step Solution:

1. **Identify the series**:
The series is: 120, 121, 117, 126, 110, ?

2. **Calculate the differences**:
- From 120 to 121: \( 121 - 120 = +1 \)
- From 121 to 117: \( 117 - 121 = -4 \)
- From 117 to 126: \( 126 - 117 = +9 \)
- From 126 to 110: \( 110 - 126 = -16 \)

So, the differences are: +1, -4, +9, -16.

3. **Identify the pattern in differences**:
The differences alternate between addition and subtraction:
- The first difference is \( +1 \) (which is \( 1^2 \))
- The second difference is \( -4 \) (which is \( -2^2 \))
- The third difference is \( +9 \) (which is \( 3^2 \))
- The fourth difference is \( -16 \) (which is \( -4^2 \))

4. **Continue the pattern**:
The next difference should be \( +25 \) (which is \( 5^2 \)) because the pattern of squares continues.

5. **Calculate the next term**:
Since the last number in the series is 110, we add the next difference:
\[ 110 + 25 = 135 \]

6. **Conclusion**:
The value of the question mark is **135**.

### Final Answer:
The answer is **135**.