find the missing number in the following series
10, 19, 40, 77, 158, ….

Options

A. 311
B. 307
C. 301
D. 299

Explanation

To find the missing number in the series: 10, 19, 40, 77, 158, ..., we can analyze the pattern of the series step by step.

### Step 1: Identify the Pattern
We start with the numbers in the series:
- 10
- 19
- 40
- 77
- 158

We notice that the series is increasing. To find the relationship between the numbers, we can look at the differences between consecutive terms.

### Step 2: Calculate the Differences
Let's calculate the differences between each pair of consecutive numbers:
- 19 - 10 = 9
- 40 - 19 = 21
- 77 - 40 = 37
- 158 - 77 = 81

Now we have the differences:
- 9
- 21
- 37
- 81

### Step 3: Analyze the Differences
Next, we can look at the differences of these differences:
- 21 - 9 = 12
- 37 - 21 = 16
- 81 - 37 = 44

Now we have a new series of differences:
- 12
- 16
- 44

### Step 4: Calculate the Second Differences
Now, we can calculate the differences of this new series:
- 16 - 12 = 4
- 44 - 16 = 28

### Step 5: Identify the Pattern in the Second Differences
The second differences do not show a clear pattern, but we can observe that the differences between the original numbers appear to be increasing in a non-linear manner.

### Step 6: Find the Next Difference
We can see that the last difference we calculated was 81. If we look at the previous differences, we can see that they are increasing.
If we continue the pattern, we can hypothesize that the next difference could be 81 + 81 = 162.

### Step 7: Calculate the Next Number
Now we add this difference to the last number in the series:
- 158 + 162 = 320

### Conclusion
Thus, the missing number in the series is **320**.