50 successive discounts of `2%,4%,6%,8%` and so on will result in a single discount of:

Options

A. `150%`
B. `250%`
C. `100%`
D. `50%`

Answer

To find the single discount resulting from 50 successive discounts of 2%, 4%, 6%, 8%, and so on, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Pattern of Discounts**:
The discounts are in an arithmetic progression (AP) where the first term (a) is 2% and the common difference (d) is also 2%.

2. **Determine the Number of Terms**:
We are given that there are 50 successive discounts.

3. **Find the Last Term of the AP**:
The nth term of an arithmetic progression can be calculated using the formula:
\[ A_n = a + (n - 1)d \]
For our case:
- \( a = 2 \)
- \( d = 2 \)
- \( n = 50 \)

Plugging in these values:
\[ A_{50} = 2 + (50 - 1) \times 2 \]
\[ A_{50} = 2 + 49 \times 2 = 2 + 98 = 100 \]
Thus, the last term (the 50th discount) is 100%.

4. **Interpret the Result**:
Since the last term of the discounts is 100%, this means that after applying all the successive discounts, the total discount is equivalent to a single discount of 100%.

### Final Answer:
The single discount resulting from 50 successive discounts of 2%, 4%, 6%, 8%, and so on is **100%**.