7 8 18 57 ?

Options

A. 244
B. 174
C. 186
D. None of these

Explanation

To find the missing number in the series 7, 8, 18, 57, we need to identify the pattern in the series. Let's analyze the series step by step.

### Step 1: Identify the pattern
We will look at the differences between consecutive terms to see if there is a pattern.

- The difference between the first term (7) and the second term (8) is:
\[ 8 - 7 = 1 \]

- The difference between the second term (8) and the third term (18) is:
\[ 18 - 8 = 10 \]

- The difference between the third term (18) and the fourth term (57) is:
\[ 57 - 18 = 39 \]

So, we have the differences:
- 1 (from 7 to 8)
- 10 (from 8 to 18)
- 39 (from 18 to 57)

### Step 2: Analyze the differences
Next, let's analyze the differences we found:
- The first difference is 1.
- The second difference is 10.
- The third difference is 39.

Now, let's look at the pattern in the differences:
- From 1 to 10, the difference is \(10 - 1 = 9\).
- From 10 to 39, the difference is \(39 - 10 = 29\).

### Step 3: Identify the next difference
The differences between the differences seem to be increasing. Let's check if there is a pattern:
- The difference from 1 to 10 is 9.
- The difference from 10 to 39 is 29.

We can see that the differences are increasing by a factor of 3:
- \(9 \times 3 = 27\) (approximately)
- So, we can assume the next difference might be \(39 + 29 + 20 = 68\).

### Step 4: Calculate the next term
Now, we can calculate the next term in the series:
- The last term we have is 57.
- If we add the next difference (which we estimated to be 68) to the last term:
\[ 57 + 68 = 125 \]

### Conclusion
Thus, the missing number in the series 7, 8, 18, 57, ? is 125.