Amit gets pocket money from his father every day. Out of the pocket money, he saves ₹ 2.75 on first day and on each succeeding day he increases his saving by 25 paise. Find the amount saved by Amit on `14^(th)` day.

Options

A. ₹ 6
B. ₹ 12
C. ₹ 8
D. ₹ 10

Answer

To solve the problem step-by-step, we will follow the arithmetic progression (AP) concept since Amit's savings form a sequence where each term increases by a constant amount.

### Step 1: Identify the first term and the common difference
- The amount saved on the first day (A1) is ₹2.75.
- The increase in savings each day (common difference, D) is ₹0.25.

### Step 2: Write the formula for the nth term of an AP
The formula for the nth term (An) of an arithmetic progression is given by:
\[ A_n = A + (n - 1) \times D \]
where:
- \( A \) is the first term,
- \( n \) is the term number,
- \( D \) is the common difference.

### Step 3: Substitute the known values into the formula
We need to find the amount saved on the 14th day (A14):
- Here, \( A = 2.75 \),
- \( n = 14 \),
- \( D = 0.25 \).

Substituting these values into the formula:
\[ A_{14} = 2.75 + (14 - 1) \times 0.25 \]

### Step 4: Simplify the expression
Calculate \( (14 - 1) \):
\[ (14 - 1) = 13 \]

Now substitute this back into the equation:
\[ A_{14} = 2.75 + 13 \times 0.25 \]

### Step 5: Calculate \( 13 \times 0.25 \)
\[ 13 \times 0.25 = 3.25 \]

### Step 6: Add the results
Now add this to the first term:
\[ A_{14} = 2.75 + 3.25 = 6.00 \]

### Conclusion
The amount saved by Amit on the 14th day is ₹6.00.