Mathematics

Problem

A scholarship amount of Rs 99\,000 is to be disbursed in a fixed number of yearly instalments that increase uniformly and form an arithmetic progression. The first instalment is Rs 1500 and the last instalment is Rs 5100. a. (i) If the number of instalments is

n

and the common difference of the progression is

d

, write the expressions for the

n

th term and the sum of the progression. b. (ii) Using the values of the first and last instalments, obtain an equation that relates

d

and

n

. c. (iii) Using the total scholarship amount, set up a second equation and hence determine both the number of instalments and the common difference.

Intuitive explanation

The key is recognizing this as an arithmetic sequence problem where you know the total sum, first term, and last term—but need to find how many instalments there are. Use the arithmetic series sum formula $S_n = \frac{n(a_1 + a_n)}{2}$ to connect these quantities. Once you find $n$ , you'll have the complete picture of the payment schedule.

Intuitive explanation

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