The wrong term in the sequence 7, 28, 63 ,124, 215, 342, 511 is

Options

A. 7
B. 28
C. 124
D. 215

Answer

To find the wrong term in the sequence 7, 28, 63, 124, 215, 342, 511, we will analyze the pattern of the sequence step by step.

### Step-by-Step Solution:

1. **Identify the terms of the sequence:**
The sequence given is: 7, 28, 63, 124, 215, 342, 511.

2. **Look for a pattern:**
We will check if the terms can be expressed in terms of cubes of integers. Let's denote the position of each term in the sequence:
- First term (n=1): 7
- Second term (n=2): 28
- Third term (n=3): 63
- Fourth term (n=4): 124
- Fifth term (n=5): 215
- Sixth term (n=6): 342
- Seventh term (n=7): 511

3. **Check each term against cubes:**
- For n=1: \(2^3 - 1 = 8 - 1 = 7\)
- For n=2: \(3^3 + 1 = 27 + 1 = 28\)
- For n=3: \(4^3 - 1 = 64 - 1 = 63\)
- For n=4: \(5^3 - 1 = 125 - 1 = 124\)
- For n=5: \(6^3 - 1 = 216 - 1 = 215\)
- For n=6: \(7^3 - 1 = 343 - 1 = 342\)
- For n=7: \(8^3 - 1 = 512 - 1 = 511\)

4. **Identify the inconsistency:**
We can see that all terms follow the pattern of \(n^3 - 1\) except for the second term (28), which is calculated as \(3^3 + 1\). This is inconsistent with the pattern established by the other terms.

5. **Conclusion:**
The wrong term in the sequence is **28**.