Find the wrong term in the following number serie questions.
2,5,17,72,359,2159

Options

A. 72
B. 359
C. 5
D. 17

Answer

To find the wrong term in the number series 2, 5, 17, 72, 359, 2159, we will analyze the pattern in the series step by step.

### Step-by-Step Solution:

1. **Identify the Terms**:
The series given is: 2, 5, 17, 72, 359, 2159.

2. **Calculate Differences**:
Let's look at the differences between consecutive terms:
- From 2 to 5: \(5 - 2 = 3\)
- From 5 to 17: \(17 - 5 = 12\)
- From 17 to 72: \(72 - 17 = 55\)
- From 72 to 359: \(359 - 72 = 287\)
- From 359 to 2159: \(2159 - 359 = 1800\)

The differences are: 3, 12, 55, 287, 1800.

3. **Look for Patterns in the Differences**:
The differences are increasing significantly. Let's analyze how these differences are generated:
- Notice that \(5 = 2 \times 2 + 1\)
- Notice that \(17 = 5 \times 3 + 2\)
- Notice that \(72 = 17 \times 4 + 4\)
- Notice that \(359 = 72 \times 5 + 19\)

We can see a pattern where each term is multiplied by an increasing integer and then added to a certain number.

4. **Continue the Pattern**:
Let's apply the pattern to find the next term:
- For \(2159\), we would expect it to be \(359 \times 6 + 5\).

Calculating this:
\[ 359 \times 6 = 2154 \]
Adding 5:
\[ 2154 + 5 = 2159 \]

5. **Check the Previous Term**:
Now, let's check the term before \(359\):
- We calculated \(72 \times 5 + 19\) to get \(359\).
- However, if we check \(72\) with the previous pattern:
\[ 17 \times 4 + 4 = 72 \]
This part is consistent.

6. **Identify the Wrong Term**:
Now, let's check the term before \(72\):
- We should have \(17 \times 4 + 3\) instead of \(72\):
\[ 17 \times 4 + 3 = 68 + 3 = 71 \]
Therefore, \(72\) is incorrect.

### Conclusion:
The wrong term in the series is **72**. The correct term should be **71**.