The wrong number in the sequency 1 , 8 , 27 , 84 , 125 , 216 , 343 is

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 will 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 calculate 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. **List the Cubes**:
Now, we can list the cubes alongside the given sequence:
- \(1^3 = 1\)
- \(2^3 = 8\)
- \(3^3 = 27\)
- \(4^3 = 64\) (This is where we notice a discrepancy)
- \(5^3 = 125\)
- \(6^3 = 216\)
- \(7^3 = 343\)

3. **Compare the Sequences**:
Now, let's compare the calculated cubes with the given sequence:
- Given: 1, 8, 27, **84**, 125, 216, 343
- Expected: 1, 8, 27, **64**, 125, 216, 343

4. **Identify the Wrong Number**:
From the comparison, we can see that the number **84** in the provided sequence does not match the expected number **64**. Therefore, **84** is the wrong number in the sequence.

5. **Conclusion**:
The wrong number in the sequence is **84**.

### Final Answer:
The wrong number in the sequence is **84**.