Find out the wrong in the series 5,15,30,135,405,1215,3645.

Options

A. 3645
B. 1215
C. 405
D. 30

Answer

To find the wrong term in the series 5, 15, 30, 135, 405, 1215, 3645, we can analyze the pattern of the series step by step.

### Step-by-Step Solution:

1. **Identify the series**: The given series is 5, 15, 30, 135, 405, 1215, 3645.

2. **Look for a pattern**: We will check if there is a consistent multiplication or addition pattern between the terms.

3. **Check the first few terms**:
- From 5 to 15: \( 5 \times 3 = 15 \)
- From 15 to 30: \( 15 \times 2 = 30 \)

4. **Check the next term**:
- From 30 to 135: \( 30 \times 4.5 = 135 \) (This seems unusual as it is not a whole number multiplier)

5. **Continue checking the next terms**:
- From 135 to 405: \( 135 \times 3 = 405 \)
- From 405 to 1215: \( 405 \times 3 = 1215 \)
- From 1215 to 3645: \( 1215 \times 3 = 3645 \)

6. **Analyze the pattern**:
- The pattern seems to be multiplying by 3 after the first two terms. The first two terms are multiplied by 3 and then 2, but the transition from 30 to 135 breaks this pattern.

7. **Conclusion**: The term 30 does not fit the established pattern of multiplication by 3. Therefore, it is the wrong term in the series.

### Final Answer:
The wrong term in the series is **30**.

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