Radhika decides to save money by depositing Rs 2000 in the first month and increasing her deposit by Rs 150 every month thereafter. She continues this pattern until the total amount saved reaches Rs 61050.
(i) Express the monthly deposits as the terms of an arithmetic progression and denote the number of months by n. Write the expression for the total amount saved after n months.
(ii) Form an equation in n that represents the condition that the total savings equal Rs 61050 and hence determine the number of months for which she deposits money.
(iii) Calculate the amount she deposits in the last month.