An app earns (900) rupees on the first day and the income increases by (175) rupees each next day. What is the total income in (9) days?

Correct answer: (14400)

The direct answer is C, 14400 rupees. Daily income forms an arithmetic progression: 900, 1075, 1250, and so on. The first term is \(a=900\), the common difference is \(d=175\), and there are \(n=9\) days. Apply \(S_n=\frac{n}{2}[2a+(n-1)d]\). Thus \(S_9=\frac{9}{2}[2(900)+8(175)]\). Calculate step by step: \(2(900)=1800\), \(8(175)=1400\), and the bracket is \(3200\). Therefore \(S_9=\frac{9}{2}\times3200=9\times1600=14400\). Option A, 13800, is too small and may come from an incorrect difference or incomplete addition. Option B, 14100, does not match the AP sum. Option C, 14400, is exactly the calculated total and is correct. Option D, 14700, is too large and may result from counting an extra day or increase. The question asks total income, so we must add all nine daily incomes, not calculate only the ninth day. Exam cue: “total for 9 days” means use the sum formula, while “income on the ninth day” would require only the nth-term formula.