Mathematics
Mathematics
Problem
Meena decides to save money every month in such a way that the amounts she deposits form an arithmetic progression. She deposits Rs 1 200 in the first month and increases each month’s deposit by Rs 150. a. (i) Obtain an expression for the amount deposited in the th month. b. (ii) In which month will her single monthly deposit first exceed Rs 3 000? Show all steps clearly. c. (iii) Verify your answer in part (ii) by calculating the exact amount deposited in that month.Intuitive explanation
The key insight here is recognizing that arithmetic progressions model real-world savings patterns—each deposit follows a predictable linear rule. Since Meena increases her deposit by a constant amount each month, you're working with a sequence where the first term and common difference are given. To find totals or specific deposits, you'll use the formulas for the -th term and sum of an arithmetic progression, which let you skip calculating every single month.
Intuitive explanation
The key insight here is recognizing that arithmetic progressions model real-world savings patterns—each deposit follows a predictable linear rule. Since Meena increases her deposit by a constant amount each month, you're working with a sequence where the first term and common difference are given. To find totals or specific deposits, you'll use the formulas for the -th term and sum of an arithmetic progression, which let you skip calculating every single month.