Question

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??​

Answer 1

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

Given,

First term (a) = 20

Common difference = 15

Also,

S(n) = 3

Now, Using Formula,

S(n) = n/2{2a + (n - 1)d}

3250 = n/2{2 × 20 + (n - 1) (15)}

3250 × 2 = n{40 + 15n - 15}

6500 = n{25 + 15n}

1300 = n{5 + 3n}

3n² + 5n - 1300 = 0

3n² + 65n - 60n - 1300 = 0

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

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

n = 20, - 65/3 (Negative value is not applicable)

n = 20