Answer:
The problem statement suggests that the series of donations is arithmetic, as each student's donation increases by one as their number increases. Therefore, we can apply the formula for the sum of an arithmetic series to solve this problem.
In an arithmetic series, the sum S of n terms is given by:
S = n/2 * (a + l)
where:
- n is the number of terms (which represents the number of students in this case),
- a is the first term (in this case, the first student's number, which would be 1), and
- l is the last term (in this case, the last student's number, which we don't know yet).
Given that S = Rs. 13225, we have:
13225 = n/2 * (1 + l)
Since this is an arithmetic series starting from 1, the last term, l, is equal to n. Thus, we can substitute l with n:
13225 = n/2 * (1 + n)
Multiplying through by 2 to clear the fraction gives:
26450 = n * (1 + n)
Rearranging to a quadratic equation gives:
n^2 + n - 26450 = 0
This is a quadratic equation in the form of ax^2 + bx + c = 0. To solve for n, we can use the quadratic formula, n = [-b ± sqrt(b^2 - 4ac)] / (2a). But since n cannot be negative in this context (as it represents the number of students), we will only consider the positive root.
Applying the quadratic formula, we find that the positive root is approximately 162.5. However, the number of students must be a whole number. Therefore, the number of students is 163, because the 163rd student did not donate fully as per their number, and that's why the total amount doesn't reach the full sum for 163 students.
So, there were 163 students who donated money to the fund.