# 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 do it by using arithmetic progression. Arithmetic progression is defined as** **an** **arithmetic progression as a sequence where the differences between every two consecutive terms are the same.

## Answer: 20 months

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 = 3250 Rs

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