An employee receives a weekly training allowance that follows an arithmetic progression: ₹500 in the first week, ₹560 in the second week, ₹620 in the third week, and so on.
a. (i) Find the common difference of the allowance sequence.
b. (ii) Denote by Sn the sum of the first n weeks’ allowances. Derive an expression, in terms of n, for the sum of the allowances received from week (n+1) to week 2n inclusive.
c. (iii) Determine the least positive integer n for which the amount received from week (n+1) to week 2n exceeds ₹25000.