What will come in place of question mark (?) inthe following number series'
9 73 105 121 129 ? 135

Options

A. 13
B. 132
C. 111
D. 133

Answer

To solve the number series: 9, 73, 105, 121, 129, ?, 135, we will look for a pattern in the differences between consecutive terms.

### Step-by-Step Solution:

1. **Identify the Terms**:
The series is: 9, 73, 105, 121, 129, ?, 135.

2. **Calculate the Differences**:
- From 9 to 73:
\( 73 - 9 = 64 \)
- From 73 to 105:
\( 105 - 73 = 32 \)
- From 105 to 121:
\( 121 - 105 = 16 \)
- From 121 to 129:
\( 129 - 121 = 8 \)

Now we have the differences: 64, 32, 16, 8.

3. **Observe the Pattern in Differences**:
The differences are:
- 64 (which is \( 64 = 2^6 \))
- 32 (which is \( 32 = 2^5 \))
- 16 (which is \( 16 = 2^4 \))
- 8 (which is \( 8 = 2^3 \))

We can see that each difference is half of the previous one.

4. **Continue the Pattern**:
Following the pattern, the next difference should be:
- \( 8 / 2 = 4 \)

5. **Calculate the Next Term**:
To find the term that replaces the question mark (?), we add this difference to the last known term (129):
\[ 129 + 4 = 133 \]

6. **Verify with the Next Term**:
Now, let's check the next term:
- From 133 to 135:
\[ 135 - 133 = 2 \]
This follows the pattern of halving the previous difference (4 halved is 2).

### Conclusion:
The term that comes in place of the question mark (?) is **133**.