What will come in place of the question mark (?) in the following number series +?
2 14 38 86 ? 374

Options

A. 182
B. 176
C. 216
D. 194

Answer

To find the missing number in the series 2, 14, 38, 86, ?, 374, we can analyze the pattern in the series step by step.

### Step 1: Identify the pattern
Let's look at the differences between consecutive numbers in the series:
- From 2 to 14: \( 14 - 2 = 12 \)
- From 14 to 38: \( 38 - 14 = 24 \)
- From 38 to 86: \( 86 - 38 = 48 \)

### Step 2: Observe the differences
Now, we can see that the differences are:
- 12, 24, 48

Notice that each difference is doubling:
- \( 12 \times 2 = 24 \)
- \( 24 \times 2 = 48 \)

### Step 3: Predict the next difference
Following the pattern, the next difference should be:
- \( 48 \times 2 = 96 \)

### Step 4: Calculate the missing number
Now, we can find the missing number by adding this difference to the last known number in the series (86):
- \( 86 + 96 = 182 \)

### Step 5: Verify the next number
To confirm, we can check the next number in the series after our missing number:
- The next number after 182 should be calculated by adding the next difference, which is:
- \( 182 + 192 = 374 \) (where 192 is the next difference, double of 96)

### Conclusion
Thus, the missing number in the series is **182**.