in the following number series only one is wrong . Find out the wrong number .
`4 " "2.5 " "3.5" "6.5" "15.5" "41.25" " 126.75`

Options

A. `2.5`
B. `3.5`
C. `6.5`
D. `15.5`

Answer

To find the wrong number in the series `4, 2.5, 3.5, 6.5, 15.5, 41.25, 126.75`, we will analyze the pattern in the series step by step.

### Step-by-Step Solution:

1. **Identify the Pattern**:
- The first number is `4`.
- To get the second number `2.5`, we can see that if we multiply `4` by `0.5` and then subtract `0.5`, we get `2.5`.
- So, the first operation seems to be: \( 4 \times 0.5 = 2 \) and \( 2 + 0.5 = 2.5 \).

2. **Continue the Pattern**:
- Now, let's apply the same logic to find the next numbers:
- From `2.5` to `3.5`:
- Multiply `2.5` by `1` (next increment) and add `1`:
\[ 2.5 \times 1 + 1 = 2.5 + 1 = 3.5 \]
- From `3.5` to `6.5`:
- Multiply `3.5` by `1.5` and add `1.5`:
\[ 3.5 \times 1.5 + 1.5 = 5.25 + 1.5 = 6.75 \]
- Here we notice that the expected number is `6.75`, but the series shows `6.5`. This indicates that `6.5` might be the wrong number.

3. **Verify the Remaining Numbers**:
- Let's check the next number:
- From `6.5` to `15.5`:
- If we assume `6.5` is wrong and replace it with `6.75`, we multiply `6.75` by `2` and add `2`:
\[ 6.75 \times 2 + 2 = 13.5 + 2 = 15.5 \]
- From `15.5` to `41.25`:
- Multiply `15.5` by `2.5` and add `2.5`:
\[ 15.5 \times 2.5 + 2.5 = 38.75 + 2.5 = 41.25 \]
- From `41.25` to `126.75`:
- Multiply `41.25` by `3` and add `3`:
\[ 41.25 \times 3 + 3 = 123.75 + 3 = 126.75 \]

4. **Conclusion**:
- The calculations confirm that the number `6.5` does not fit the established pattern, as it should be `6.75`. Thus, the wrong number in the series is **6.5**.