SOLUTION: A man repays a loan of Rs.3,250 by paying Rs.305 in the first month and then decreases the payment by Rs.15 every month. How long will it take to clear his loan?

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Question 921977: A man repays a loan of Rs.3,250 by paying Rs.305 in the first month and then decreases the payment by Rs.15 every month. How long will it take to clear his loan?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
General term of sequence, 305-%28n-1%2915. The last allowable term must be 305=15%28n-1%29
305=15n-15
320=15n
n=21 for practical purposes. Cannot allow for more than 21 monthly payments.

You want to know for what sum of consecutive terms the loan of Rs 3250 will be paid.

%28n%2F2%29%28305%2B%28305-15%28n-1%29%29%29 compared to 3250;
And remember n%3C=21.

%28n%2F2%29%28610-15%28n-1%29%29=3250
the steps will lead to
3n%5E2-125n%2B1300=0
and the discriminant is 25.

Directly using general solution of a quadratic equation,
n=%28125%2B-+sqrt%2825%29%29%2F%282%2A3%29
simplifying to either highlight%28n=20%29 or n=21%262%2F3.

Only one of those makes the right kind of sense. Remember, n must not be more than 21.
n=20, meaning twenty monthly payments will finish the debt.