If you save Rs. 1 today, Rs. 2 the next day, Rs. 3 the succeeding day and so on, what will be your total savings in 365 days?

Options

A. 66579
B. 66795
C. 56795
D. none of these

Answer

To find the total savings after saving Rs. 1 on the first day, Rs. 2 on the second day, and so on up to Rs. 365 on the 365th day, we can use the formula for the sum of the first n natural numbers. Here’s how to solve the problem step by step:

### Step-by-Step Solution:

1. **Identify the Pattern**:
- On day 1, you save Rs. 1.
- On day 2, you save Rs. 2.
- On day 3, you save Rs. 3.
- This continues until day 365 where you save Rs. 365.

2. **Recognize the Sequence**:
- The amount saved each day forms an arithmetic series where:
- First term (a) = 1
- Last term (l) = 365
- Number of terms (n) = 365

3. **Use the Formula for the Sum of an Arithmetic Series**:
- The formula to calculate the sum \( S_n \) of the first n terms of an arithmetic series is:
\[ S_n = \frac{n}{2} \times (a + l) \]
- Here, \( a \) is the first term, \( l \) is the last term, and \( n \) is the number of terms.

4. **Substitute the Values**:
- Substitute \( n = 365 \), \( a = 1 \), and \( l = 365 \) into the formula:
\[ S_{365} = \frac{365}{2} \times (1 + 365) \]

5. **Calculate the Sum**:
- First, calculate \( 1 + 365 = 366 \).
- Now, substitute back:
\[ S_{365} = \frac{365}{2} \times 366 \]
- Calculate \( \frac{365 \times 366}{2} \):
\[ S_{365} = \frac{133590}{2} = 66795 \]

6. **Final Result**:
- Therefore, the total savings after 365 days is Rs. 66795.

### Final Answer:
The total savings in 365 days is Rs. 66795.