3, 15, 35, 63, 99, ….

Options

A. 133
B. 137
C. 139
D. 143

Explanation

To find the next number in the series 3, 15, 35, 63, 99, we will analyze the differences between consecutive terms and look for a pattern.

### Step 1: Identify the differences between consecutive terms.
- The difference between the first and second term (15 - 3) is **12**.
- The difference between the second and third term (35 - 15) is **20**.
- The difference between the third and fourth term (63 - 35) is **28**.
- The difference between the fourth and fifth term (99 - 63) is **36**.

So, the differences are: 12, 20, 28, 36.

### Step 2: Identify the differences of the differences.
Now, let's find the differences of these differences:
- The difference between the first and second difference (20 - 12) is **8**.
- The difference between the second and third difference (28 - 20) is **8**.
- The difference between the third and fourth difference (36 - 28) is **8**.

So, the second-level differences are: 8, 8, 8.

### Step 3: Predict the next difference.
Since the second-level differences are constant (8), we can predict the next first-level difference by adding 8 to the last first-level difference:
- The last first-level difference is 36, so the next difference will be **36 + 8 = 44**.

### Step 4: Calculate the next term in the series.
Now, we will add this new difference (44) to the last term in the series (99):
- The next term will be **99 + 44 = 143**.

### Conclusion:
Thus, the next number in the series is **143**.