What will come in place of question mark (?) in the given number series questions?
14 30 66 130 230 ?

Options

A. 374
B. 378
C. 382
D. 364

Answer

To find the missing number in the series: 14, 30, 66, 130, 230, ?, we will analyze the differences between the consecutive numbers.

**Step 1: Calculate the differences between the consecutive numbers.**
- Difference between 30 and 14:
\( 30 - 14 = 16 \)

- Difference between 66 and 30:
\( 66 - 30 = 36 \)

- Difference between 130 and 66:
\( 130 - 66 = 64 \)

- Difference between 230 and 130:
\( 230 - 130 = 100 \)

So, the differences are: 16, 36, 64, 100.

**Step 2: Analyze the differences.**
Now, let's look at the differences we calculated:
- 16 = \( 4^2 \)
- 36 = \( 6^2 \)
- 64 = \( 8^2 \)
- 100 = \( 10^2 \)

We can see that the differences are squares of even numbers: \( 4, 6, 8, 10 \).

**Step 3: Identify the pattern in the squares.**
The even numbers are increasing by 2:
- The next even number after 10 is 12.

**Step 4: Calculate the next difference.**
Now, we will find the square of 12:
- \( 12^2 = 144 \)

**Step 5: Add the next difference to the last number in the series.**
Now we will add this difference to the last number in the series:
- \( 230 + 144 = 374 \)

Thus, the missing number in the series is **374**.

### Final Answer:
The number that comes in place of the question mark (?) is **374**.