# A man repays a loan of Rs. 3250 by paying Rs. 20 in the first month and then increases the payment by Rs 15 every month. How long will it take him to clear the loan?

We can solve this by using arithmetic progression. Arithmetic progression is defined as** **a sequence where the difference between every two consecutive terms is the same.

## Answer: It will take him 20 months to clear the loan.

We will use the formula of Sum of 'n' terms of an AP. The formula is given by S_{n}= n/2 [2a + (n - 1) d].

**Explanation:**

Let 'n' be the loan cleared in 'n' months.

Amounts are in the form of AP with first term (a) = 20 and common difference (d) = 15

Total amount = Rs 3250

S_{n} = n/2 [2a + (n - 1)d]

3250 = n/2 [2(20) + (n - 1)15]

3250 = n/2 [40 + 15n - 15]

6500 = n [15n + 25]

15n^{2} + 25n - 6500 = 0

3n^{2} + 5n - 1300 = 0

3n^{2} + 65n - 60n - 1300 = 0

n (3n + 65) -20 (3n + 65) = 0

(n - 20) (3n + 65) = 0

n = 20 and n = -65/3

Here, the months cannot be negative. So, we take n = 20