Find out the wrong number in the following sequence of numbers
1,8,27,84,125,216,343.

Options

A. 1
B. 27
C. 84
D. 216

Answer

To find the wrong number in the sequence 1, 8, 27, 84, 125, 216, 343, we can analyze the pattern of the numbers.

### Step-by-Step Solution:

1. **Identify the Pattern**:
The sequence appears to be related to the cubes of natural numbers. Let's list the cubes of the first few natural numbers:
- \(1^3 = 1\)
- \(2^3 = 8\)
- \(3^3 = 27\)
- \(4^3 = 64\)
- \(5^3 = 125\)
- \(6^3 = 216\)
- \(7^3 = 343\)

2. **Compare with the Given Sequence**:
Now, let's compare the cubes we calculated with the given sequence:
- Given sequence: 1, 8, 27, 84, 125, 216, 343
- Cubes: 1, 8, 27, 64, 125, 216, 343

3. **Identify the Anomaly**:
From the comparison, we can see that the fourth number in the given sequence is 84, while the fourth cube (which should be present in the sequence) is 64. Therefore, 84 does not fit the pattern of cubes.

4. **Conclusion**:
The wrong number in the sequence is **84**. It should be replaced with **64** to maintain the pattern of cubes.