what should come in place of question mark 2 7 22 67 202 ?

Options

A. 364
B. 428
C. 598
D. 607

Answer

To find the missing number in the series: 2, 7, 22, 67, 202, ?, we can analyze the pattern of the series step by step.

### Step 1: Identify the series
The series given is:
2, 7, 22, 67, 202, ?

### Step 2: Find the differences between consecutive terms
Let's calculate the differences between each pair of consecutive terms:
- 7 - 2 = 5
- 22 - 7 = 15
- 67 - 22 = 45
- 202 - 67 = 135

So, the differences are:
5, 15, 45, 135

### Step 3: Identify the pattern in the differences
Now, let's look at the differences:
- 5 = 5
- 15 = 5 * 3
- 45 = 15 * 3
- 135 = 45 * 3

We can see that each difference is multiplied by 3 to get the next difference.

### Step 4: Calculate the next difference
To find the next difference, we multiply the last difference (135) by 3:
135 * 3 = 405

### Step 5: Add the next difference to the last term in the series
Now, we add this difference to the last term in the series (202):
202 + 405 = 607

### Conclusion
Thus, the missing number in the series is **607**.