A series is given with one wrong term. Choose the wrong alternative from the given ones :
3, 6, 16, 47.5, 154.5, 558.5
निम्नलिखित प्रत्येक प्रश्न में एक अनुक्रम दिया है, जिसमें एक पद गलत है। दिये गये विकल्पों में से गलत विकल्प चुनिये :
3, 6, 16, 47.5, 154.5, 558.5

Options

A. `16`
B. `47.5 `
C. `154.5`
D. `558.5 `

Explanation

To identify the wrong term in the series 3, 6, 16, 47.5, 154.5, 558.5, we will analyze the pattern of the series step by step.

### Step 1: Identify the first term and the operation to get to the second term.
- The first term is 3.
- To get to the second term (6), we can observe that:
\[ 3 \times 1.5 = 4.5 \quad \text{(not quite right)} \]
Instead, we can add:
\[ 3 + 3 = 6 \]

**Hint:** Check simple operations like addition or multiplication to see how the terms relate.

### Step 2: Identify the operation to get from the second term to the third term.
- The second term is 6.
- To get to the third term (16):
\[ 6 \times 2 + 4 = 12 + 4 = 16 \]

**Hint:** Look for a consistent pattern in how each term is derived from the previous one.

### Step 3: Identify the operation to get from the third term to the fourth term.
- The third term is 16.
- To get to the fourth term (47.5):
\[ 16 \times 2.5 + 4 = 40 + 7.5 = 47.5 \]

**Hint:** Continue applying the same logic to see if the pattern holds.

### Step 4: Identify the operation to get from the fourth term to the fifth term.
- The fourth term is 47.5.
- To get to the fifth term (154.5):
\[ 47.5 \times 3 + 4 = 142.5 + 12 = 154.5 \]

**Hint:** Check if the multiplication factor is increasing consistently.

### Step 5: Identify the operation to get from the fifth term to the sixth term.
- The fifth term is 154.5.
- To get to the sixth term (558.5):
\[ 154.5 \times 3.5 + 4 = 541.75 + 16.75 = 558.5 \]

**Hint:** Ensure that the pattern of multiplication and addition is consistent throughout the series.

### Conclusion:
After analyzing the series, we find that the operation from 47.5 to 154.5 is consistent, but the operation from 154.5 to 558.5 is incorrect. The correct term should follow the pattern of multiplying by an increasing factor and adding a constant.

The term 154.5 is correct, but the term 558.5 does not follow the expected pattern based on the previous terms.

Thus, the wrong term in the series is **558.5**.

**Final Answer:** The wrong term is **558.5**.