In each of the following questions a series is given. In each one term is wrong. Find out the wrong term
4, 5, 9, 29, 111, 556, 3335

Options

A. 5
B. 9
C. 29
D. 111

Answer

To find the wrong term in the series 4, 5, 9, 29, 111, 556, 3335, we will analyze the pattern of the series step by step.

### Step 1: Identify the pattern
Let's look at the differences between the terms and see if there is a consistent pattern.

- From 4 to 5: \(5 = 4 + 1\)
- From 5 to 9: \(9 = 5 + 4\)
- From 9 to 29: \(29 = 9 + 20\)
- From 29 to 111: \(111 = 29 + 82\)
- From 111 to 556: \(556 = 111 + 445\)
- From 556 to 3335: \(3335 = 556 + 2779\)

### Step 2: Analyze the differences
Now, let's analyze the differences we calculated:

- \(5 - 4 = 1\)
- \(9 - 5 = 4\)
- \(29 - 9 = 20\)
- \(111 - 29 = 82\)
- \(556 - 111 = 445\)
- \(3335 - 556 = 2779\)

### Step 3: Look for a multiplication pattern
Next, we will check if there is a multiplication pattern involved:

1. \(4 \times 1 + 1 = 5\)
2. \(5 \times 2 - 1 = 9\)
3. \(9 \times 3 + 2 = 29\)
4. \(29 \times 4 - 2 = 111\)
5. \(111 \times 5 + 5 = 556\)
6. \(556 \times 6 - 6 = 3335\)

### Step 4: Identify the wrong term
Now, we can see that the pattern is alternating between adding and subtracting a number that is increasing. However, when we check the term \(29\):

- According to the pattern, it should be \(9 \times 3 + 2 = 29\) (which is correct).
- But for \(111\), it should be \(29 \times 4 - 2 = 114\) (not 111).

Thus, the term \(111\) does not fit the pattern and is the wrong term.

### Conclusion
The wrong term in the series is **111**.

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