In each of the following questions, find the wrong term in the given series.
2,12,36,80,150,251,392

Options

A. 36
B. 80
C. 251
D. 392

Answer

To find the wrong term in the series 2, 12, 36, 80, 150, 251, 392, we will analyze the pattern of the series step by step.

### Step 1: Identify the Pattern
We need to find a pattern in the series. One way to do this is to express each term in relation to squares and cubes of integers.

### Step 2: Analyze Each Term
1. **First Term (2)**:
- \(1^2 + 1^3 = 1 + 1 = 2\)

2. **Second Term (12)**:
- \(2^2 + 2^3 = 4 + 8 = 12\)

3. **Third Term (36)**:
- \(3^2 + 3^3 = 9 + 27 = 36\)

4. **Fourth Term (80)**:
- \(4^2 + 4^3 = 16 + 64 = 80\)

5. **Fifth Term (150)**:
- \(5^2 + 5^3 = 25 + 125 = 150\)

6. **Sixth Term (251)**:
- \(6^2 + 6^3 = 36 + 216 = 252\) (This is where we notice a discrepancy)

7. **Seventh Term (392)**:
- \(7^2 + 7^3 = 49 + 343 = 392\)

### Step 3: Identify the Wrong Term
From the calculations, we see that the sixth term should be 252, but it is given as 251 in the series. Therefore, 251 is the wrong term.

### Conclusion
The wrong term in the series is **251**.

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