What will come in place of question mark(?) in the given number series?
3 72 129 173 203 ?

Options

A. 227
B. 254
C. 252
D. 218

Answer

To solve the number series: 3, 72, 129, 173, 203, ?, we need to identify the pattern in the differences between the consecutive numbers.

### Step 1: Find the differences between consecutive terms.
- Difference between 72 and 3:
\[ 72 - 3 = 69 \]
- Difference between 129 and 72:
\[ 129 - 72 = 57 \]
- Difference between 173 and 129:
\[ 173 - 129 = 44 \]
- Difference between 203 and 173:
\[ 203 - 173 = 30 \]

### Step 2: List the differences.
The differences we found are:
- 69, 57, 44, 30

### Step 3: Find the differences of the differences.
Now, we will find the differences between these differences:
- Difference between 57 and 69:
\[ 57 - 69 = -12 \]
- Difference between 44 and 57:
\[ 44 - 57 = -13 \]
- Difference between 30 and 44:
\[ 30 - 44 = -14 \]

### Step 4: List the second differences.
The second differences are:
- -12, -13, -14

### Step 5: Find the next difference in the second differences.
The pattern in the second differences shows that they are decreasing by 1 each time. Therefore, the next difference would be:
\[ -14 - 1 = -15 \]

### Step 6: Find the next difference in the first differences.
Now we will subtract this from the last first difference (30):
\[ 30 - 15 = 15 \]

### Step 7: Find the next term in the series.
Now we will add this difference to the last term in the original series (203):
\[ 203 + 15 = 218 \]

Thus, the number that will come in place of the question mark (?) is **218**.

### Final Answer:
The answer is **218**.