Find the missing term in the following numbers series:
5,15,50,?,1030,6185

Options

A. 210
B. 205
C. 225
D. 200

Answer

To find the missing term in the series 5, 15, 50, ?, 1030, 6185, we can follow these steps:

### Step 1: Identify the pattern
We will analyze how each term relates to the previous term.

- The first term is 5.
- The second term is 15.
- The third term is 50.

### Step 2: Calculate the relationship between terms
Let's look at how we can get from one term to the next:

1. From 5 to 15:
\[ 5 \times 2 + 5 = 15 \]

2. From 15 to 50:
\[ 15 \times 3 + 5 = 50 \]

3. Now, we need to find the fourth term (let's call it \( x \)):
\[ 50 \times 4 + 5 = x \]

### Step 3: Calculate the fourth term
Now we can calculate \( x \):
\[ x = 50 \times 4 + 5 = 200 + 5 = 205 \]

### Step 4: Verify the pattern with the next terms
Now, let's verify if this pattern holds for the next terms:

4. From \( x \) (which is 205) to 1030:
\[ 205 \times 5 + 5 = 1025 + 5 = 1030 \]

5. From 1030 to 6185:
\[ 1030 \times 6 + 5 = 6180 + 5 = 6185 \]

### Conclusion
The missing term in the series is **205**.