Find the wrong term
5, 17, 37, 65, 101, 155

Options

A. 17
B. 65
C. 101
D. 155

Explanation

To find the wrong term in the series 5, 17, 37, 65, 101, 155, we will analyze the differences between the terms step by step.

### Step 1: Identify the given series
The series is:
5, 17, 37, 65, 101, 155

### Step 2: Calculate the differences between consecutive terms
- Difference between 17 and 5:
\( 17 - 5 = 12 \)

- Difference between 37 and 17:
\( 37 - 17 = 20 \)

- Difference between 65 and 37:
\( 65 - 37 = 28 \)

- Difference between 101 and 65:
\( 101 - 65 = 36 \)

- Difference between 155 and 101:
\( 155 - 101 = 54 \)

Now we have the first differences:
12, 20, 28, 36, 54

### Step 3: Calculate the differences of the first differences
Now, let's find the differences of these first differences:
- Difference between 20 and 12:
\( 20 - 12 = 8 \)

- Difference between 28 and 20:
\( 28 - 20 = 8 \)

- Difference between 36 and 28:
\( 36 - 28 = 8 \)

- Difference between 54 and 36:
\( 54 - 36 = 18 \)

Now we have the second differences:
8, 8, 8, 18

### Step 4: Analyze the second differences
We can see that the second differences are not consistent. The first three second differences are 8, but the last one is 18. This indicates that there is a mistake in the series.

### Step 5: Determine the correct term
Since the second difference should be consistent, we can assume that the difference between the last two first differences should also be 8. Therefore, the expected first difference before 54 should be:
\( 36 + 8 = 44 \)

### Step 6: Calculate the correct term
If the correct first difference before 155 is 44, then the term before 155 should be:
\( 101 + 44 = 145 \)

### Conclusion
Thus, the wrong term in the series is 155. The correct term should be 145.

### Final Answer
The wrong term is **155**.

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