which number in the following series is wrong?
574,286,142,72,34,16,7

Options

A. 286
B. 142
C. 72
D. 34

Answer

To determine which number in the series 574, 286, 142, 72, 34, 16, 7 is incorrect, we can analyze the pattern in the series.

### Step-by-Step Solution:

1. **Identify the Pattern**: We will start from the last number in the series and move upwards to see if there is a consistent pattern.

2. **Check the Last Number**: Starting with 7:
- Multiply 7 by 2:
\[ 7 \times 2 = 14 \]
- Add 2:
\[ 14 + 2 = 16 \]
- This checks out since the next number in the series is 16.

3. **Move to the Next Number**: Now, take 16:
- Multiply 16 by 2:
\[ 16 \times 2 = 32 \]
- Add 2:
\[ 32 + 2 = 34 \]
- This also checks out since the next number in the series is 34.

4. **Continue the Pattern**: Now, take 34:
- Multiply 34 by 2:
\[ 34 \times 2 = 68 \]
- Add 2:
\[ 68 + 2 = 70 \]
- Here, we see that the expected result is 70, but the next number in the series is 72.

5. **Check the Next Number**: Let's check 72:
- If we multiply 72 by 2:
\[ 72 \times 2 = 144 \]
- Add 2:
\[ 144 + 2 = 146 \]
- This does not match the next number (34) in our series.

6. **Conclusion**: Since the pattern indicates that the number following 34 should be 70, and not 72, we conclude that 72 is the incorrect number in the series.

### Final Answer:
The wrong number in the series is **72**.