**Q) **Rohan repays his total loan of Rs.1,18,000 by paying every month starting with the first installment of Rs. 1,000. If he increases the installment by Rs. 100 every month, what amount will be paid by him in the 30^{th} installment? What amount of loan has he paid after 30^{th} installment?

**Ans: **

We can see that the loan repayment forms an A. P., where:

a = 1,000, d = 100, Sum of AP = 1,18,000

Let’s start from value of the 30^{th} term (i.e. amount paid in this installment).

We know that n^{th} term of an A.P. = a + (n-1) d

Therefore, T_{30}

= 1000 + (30 – 1) x 100 = 3900

**Therefore, the amount paid in 30 ^{th} installment is Rs. 3,900.**

Next, sum of n terms of an A.P. S_{n }= (2a + (n-1) d)

Therefore, S_{30 }= (2 x 1000 + (30 – 1) x 100)

= 15 (2000 + 2900) = 73500

**Therefore the loan paid after 30 ^{th} installment is Rs. 73,500.**