A public library charges its members an annual subscription fee. The fee was ₹350 in the first year and is planned to rise by ₹5 every subsequent year.
a. (i) Explain why the sequence of annual fees forms a pattern with a constant difference, and state the first term as well as the common difference.
b. (ii) Derive a formula for the subscription fee payable in the nth year.
c. (iii) In which year will the cumulative amount paid by a member since joining first exceed ₹1,200? Show complete working.