On March 1st 2016, Sherry saved 1. Everyday starting from March 2nd 2016, he save 1 more than the previous day. Find the first date after March 1st 2016 at the end of which his total savings will be a perfect square.

Options

A. A)17th March 2016
B. B)18th April 2016
C. C)26th March 2016
D. D)None of these

Answer

To solve the problem step by step, we need to determine the total savings of Sherry over a series of days and find the first date after March 1st, 2016, when the total savings will be a perfect square.

### Step 1: Understand the savings pattern
Sherry saves 1 rupee on March 1st, 2016. Starting from March 2nd, he saves 1 rupee more than the previous day. This means:
- On March 1st: 1 rupee
- On March 2nd: 2 rupees
- On March 3rd: 3 rupees
- On March 4th: 4 rupees
- ...
- On March n: n rupees

### Step 2: Calculate total savings after n days
The total savings after n days can be calculated using the formula for the sum of the first n natural numbers:
\[ S_n = 1 + 2 + 3 + ... + n = \frac{n(n + 1)}{2} \]

### Step 3: Identify the first perfect square
We need to find the smallest value of n such that \( S_n \) is a perfect square. This means we need to check values of n starting from 1 and see if \( \frac{n(n + 1)}{2} \) is a perfect square.

### Step 4: Check values of n
1. For \( n = 1 \):
\[ S_1 = \frac{1(1 + 1)}{2} = 1 \quad (\text{Perfect square: } 1^2) \]
Date: March 1, 2016

2. For \( n = 2 \):
\[ S_2 = \frac{2(2 + 1)}{2} = 3 \quad (\text{Not a perfect square}) \]

3. For \( n = 3 \):
\[ S_3 = \frac{3(3 + 1)}{2} = 6 \quad (\text{Not a perfect square}) \]

4. For \( n = 4 \):
\[ S_4 = \frac{4(4 + 1)}{2} = 10 \quad (\text{Not a perfect square}) \]

5. For \( n = 5 \):
\[ S_5 = \frac{5(5 + 1)}{2} = 15 \quad (\text{Not a perfect square}) \]

6. For \( n = 6 \):
\[ S_6 = \frac{6(6 + 1)}{2} = 21 \quad (\text{Not a perfect square}) \]

7. For \( n = 7 \):
\[ S_7 = \frac{7(7 + 1)}{2} = 28 \quad (\text{Not a perfect square}) \]

8. For \( n = 8 \):
\[ S_8 = \frac{8(8 + 1)}{2} = 36 \quad (\text{Perfect square: } 6^2) \]
Date: March 8, 2016

### Conclusion
The first date after March 1st, 2016, at the end of which Sherry's total savings will be a perfect square is **March 8, 2016**.