A man starts repaying a loan as first instalment of Rs. 100. If the increases the instalment by Rs. 5 every month, then the amount he will pay in the 30th instalment is

Options

A. 245
B. 345
C. 445
D. 550

Answer

To solve the problem of determining the amount the man will pay in the 30th installment of his loan repayment, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the first installment and the common difference**:
- The first installment (A) is Rs. 100.
- The installment increases by Rs. 5 every month, which means the common difference (D) is Rs. 5.

2. **Recognize the sequence type**:
- The installments form an arithmetic progression (AP) because each installment increases by a constant amount (D).

3. **Use the formula for the nth term of an AP**:
- The formula for the nth term (Tn) of an arithmetic progression is given by:
\[ T_n = A + (n - 1) \times D \]
- Here, we need to find the 30th term (T30), so we will substitute n = 30 into the formula.

4. **Substitute the values into the formula**:
- Substitute A = 100, D = 5, and n = 30 into the formula:
\[ T_{30} = 100 + (30 - 1) \times 5 \]

5. **Calculate the expression**:
- Simplify the expression:
\[ T_{30} = 100 + 29 \times 5 \]
- Calculate \(29 \times 5\):
\[ 29 \times 5 = 145 \]
- Now add this to 100:
\[ T_{30} = 100 + 145 = 245 \]

6. **Conclusion**:
- Therefore, the amount he will pay in the 30th installment is Rs. 245.

### Final Answer:
The amount he will pay in the 30th installment is **Rs. 245**.