What will come in place of question mark (?) in the given number series questions?
7 14 40 103 ? 442

Options

A. 225
B. 235
C. 218
D. 227

Answer

To find the missing number in the series: 7, 14, 40, 103, ?, 442, we will analyze the differences between the consecutive terms and look for a pattern.

### Step 1: Find the differences between the consecutive terms.
- The difference between 14 and 7 is:
\[ 14 - 7 = 7 \]
- The difference between 40 and 14 is:
\[ 40 - 14 = 26 \]
- The difference between 103 and 40 is:
\[ 103 - 40 = 63 \]

Now we have the first set of differences:
- 7, 26, 63

### Step 2: Find the differences of the differences.
Next, we will find the differences of these differences:
- The difference between 26 and 7 is:
\[ 26 - 7 = 19 \]
- The difference between 63 and 26 is:
\[ 63 - 26 = 37 \]

Now we have the second set of differences:
- 19, 37

### Step 3: Find the differences of the second differences.
Now, we will find the differences of the second differences:
- The difference between 37 and 19 is:
\[ 37 - 19 = 18 \]

Now we have the third set of differences:
- 18

### Step 4: Predict the next difference.
Since the third difference is constant (18), we can predict the next second difference:
- The next second difference after 37 will be:
\[ 37 + 18 = 55 \]

### Step 5: Predict the next first difference.
Now, we can predict the next first difference:
- The next first difference after 63 will be:
\[ 63 + 55 = 118 \]

### Step 6: Find the missing term.
Now we can find the missing term in the original series:
- The missing term (let's call it x) can be found by adding the last known term (103) to the next first difference (118):
\[ x = 103 + 118 = 221 \]

### Step 7: Verify with the next term in the series.
Now we can verify by calculating the difference between the next term (442) and the missing term (221):
- The difference should be:
\[ 442 - 221 = 221 \]

### Conclusion:
Thus, the missing number in the series is:
\[ \boxed{221} \]