Find the wrong number in the given series.
84,83,79,70,52,29

Answer

To find the wrong number in the series 84, 83, 79, 70, 52, 29, we will analyze the differences between the consecutive numbers and look for a pattern.

### Step-by-Step Solution:

1. **Identify the Series**: We have the series: 84, 83, 79, 70, 52, 29.

2. **Calculate the Differences**:
- 84 to 83: \( 84 - 83 = 1 \)
- 83 to 79: \( 83 - 79 = 4 \)
- 79 to 70: \( 79 - 70 = 9 \)
- 70 to 52: \( 70 - 52 = 18 \)
- 52 to 29: \( 52 - 29 = 23 \)

3. **List the Differences**: The differences we calculated are:
- 1, 4, 9, 18, 23

4. **Look for a Pattern**:
- The differences do not seem to follow a clear arithmetic or geometric pattern at first glance. However, if we observe the differences closely:
- The first difference is \( 1 = 1^2 \)
- The second difference is \( 4 = 2^2 \)
- The third difference is \( 9 = 3^2 \)
- The fourth difference is \( 18 \) (which does not fit the pattern of squares)
- The fifth difference is \( 23 \)

5. **Identify the Anomaly**: The difference of \( 18 \) does not fit the pattern of being a perfect square. The expected difference after \( 9 \) (which is \( 3^2 \)) should be \( 16 \) (which is \( 4^2 \)).

6. **Find the Wrong Number**:
- If we replace \( 70 \) with \( 64 \) (which would be \( 79 - 16 \)), the series would then be:
- 84, 83, 79, 64, 52, 29
- The differences would then be:
- 1, 4, 15, 12, 23
- This still does not fit a clear pattern, but it indicates that \( 70 \) is the wrong number as it disrupts the expected pattern of differences.

7. **Conclusion**: The wrong number in the series is \( 70 \).