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?

Suppose the loan is cleared in n months. Clearly, the amounts form an A.P. with the first term 20 and the common difference 15.

∴ Sum of the amounts  = 3250

⟹ n/2 {2 × 20 + (n−1) × 15} = 3250

⟹ n/2 (40 + 15n −1 5) = 3250

⟹ n (15n + 25) = 6500

⟹ 15² + 25n − 6500 = 0

⟹ 3n² + 5n − 1300 = 0

⟹ (n − 20) (3n + 65) = 0

⟹ n = 20 or, n = −65/3  ⟹ n = 20

Hence, the loan is cleared in $20$ months.

Watch the video for more information on arithmetic progression

Further reference

• The sum S_n of the terms of an arithmetic progression is defined by the formula
• Write first four terms of the A.P. when the first term a and the common difference are given as follows: (i) a = 10, d = 10 (ii) a = -2, d = 0 (iii) a = 4, d = – 3 (iv) a = -1 d = 1/2 (v) a = – 1.25, d = – 0.25