What will come in place of questions mark (?) in the following number series ?
`"24 51 99 201 399 ?"`

Options

A. 789
B. 810
C. 798
D. 801

Answer

To find the missing number in the series: 24, 51, 99, 201, 399, ?, we will analyze the pattern in the series step by step.

### Step 1: Identify the pattern
Let's look at the differences between consecutive terms in the series.

- From 24 to 51:
\( 51 - 24 = 27 \)

- From 51 to 99:
\( 99 - 51 = 48 \)

- From 99 to 201:
\( 201 - 99 = 102 \)

- From 201 to 399:
\( 399 - 201 = 198 \)

So, the differences are: 27, 48, 102, 198.

### Step 2: Analyze the differences
Now, let's look at the differences of the differences:

- From 27 to 48:
\( 48 - 27 = 21 \)

- From 48 to 102:
\( 102 - 48 = 54 \)

- From 102 to 198:
\( 198 - 102 = 96 \)

The second differences are: 21, 54, 96.

### Step 3: Analyze the second differences
Now, let's look at the differences of the second differences:

- From 21 to 54:
\( 54 - 21 = 33 \)

- From 54 to 96:
\( 96 - 54 = 42 \)

The third differences are: 33, 42.

### Step 4: Predict the next difference
From the pattern observed, the differences seem to be increasing. If we continue this pattern, we can assume the next difference will be:

- The next difference after 42 could be \( 42 + 9 = 51 \).

### Step 5: Calculate the next second difference
Now, we can add this to the last second difference:

- Next second difference:
\( 96 + 51 = 147 \).

### Step 6: Calculate the next first difference
Now, we can add this to the last first difference:

- Next first difference:
\( 198 + 147 = 345 \).

### Step 7: Calculate the next term in the series
Now, we can add this to the last term in the series:

- Next term:
\( 399 + 345 = 744 \).

Thus, the number that will come in place of the question mark (?) in the series is **744**.

### Final Answer:
The missing number is **744**.

---