Amit saves certain amount every month in a specific way. In the first month he saves Rupees 200, in the second month Rupees 250. In the third month Rupees 300 and so on . How much will be his total saving in 17 months ?

Explanation

To find Amit's total savings over 17 months, we can recognize that the amounts he saves each month 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 first term (A) of the AP is the amount saved in the first month, which is Rs. 200.
- The second term is Rs. 250, and the third term is Rs. 300.
- The common difference (D) can be calculated as:
\[ D = 250 - 200 = 50 \]

### Step 2: Use the formula for the sum of the first N terms of an AP
The formula for the sum of the first N terms (S_N) of an arithmetic progression is given by:
\[ S_N = \frac{N}{2} \times (2A + (N - 1)D) \]
Where:
- \(N\) is the number of terms (in this case, 17),
- \(A\) is the first term (200),
- \(D\) is the common difference (50).

### Step 3: Substitute the values into the formula
Now, we can substitute the values into the formula:
\[ S_{17} = \frac{17}{2} \times (2 \times 200 + (17 - 1) \times 50) \]

### Step 4: Simplify the equation
Calculate the expression inside the parentheses:
\[ 2 \times 200 = 400 \]
\[ (17 - 1) \times 50 = 16 \times 50 = 800 \]
Now substitute these values back into the equation:
\[ S_{17} = \frac{17}{2} \times (400 + 800) \]
\[ S_{17} = \frac{17}{2} \times 1200 \]

### Step 5: Calculate the total savings
Now, calculate:
\[ S_{17} = \frac{17 \times 1200}{2} = \frac{20400}{2} = 10200 \]

### Conclusion
Amit's total savings after 17 months will be Rs. 10,200.

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