Daya gets pocket money from his father every day. Out of the pocket money, he saves Rs 2.75 on first day, Rs 3.00 on second day, Rs 3.25 on third day and so on. Find:
the amount saved by Daya on `14^(th)` day

Answer

To find the amount saved by Daya on the 14th day, we can observe that the amounts he saves each day form an arithmetic progression (AP). Let's break down the solution step by step.

### Step 1: Identify the first term and the common difference
The amount saved by Daya on each day is as follows:
- 1st day: Rs 2.75
- 2nd day: Rs 3.00
- 3rd day: Rs 3.25

From this, we can see:
- First term (a) = 2.75
- Second term = 3.00
- Third term = 3.25

To find the common difference (d):
\[ d = \text{Second term} - \text{First term} = 3.00 - 2.75 = 0.25 \]
So, the common difference \( d = 0.25 \).

### Step 2: Use the formula for the nth term of an AP
The formula for the nth term of an arithmetic progression is given by:
\[ a_n = a + (n - 1) \cdot d \]
where:
- \( a \) is the first term,
- \( n \) is the term number,
- \( d \) is the common difference.

### Step 3: Substitute the values into the formula
We need to find the amount saved on the 14th day, so we set \( n = 14 \):
\[ a_{14} = 2.75 + (14 - 1) \cdot 0.25 \]
This simplifies to:
\[ a_{14} = 2.75 + 13 \cdot 0.25 \]

### Step 4: Calculate the value
Now, calculate \( 13 \cdot 0.25 \):
\[ 13 \cdot 0.25 = 3.25 \]
Now, substitute this back into the equation:
\[ a_{14} = 2.75 + 3.25 \]
\[ a_{14} = 6.00 \]

### Conclusion
Thus, the amount saved by Daya on the 14th day is **Rs 6.00**.

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