An app earns (500) rupees on the first day and the income increases by (100) rupees each next day. What is the total income in (10) days?

Correct answer: (9500)

The direct answer is C: ₹9,500. The daily incomes form an arithmetic progression because the first income is ₹500 and the same amount, ₹100, is added each day. Thus, the first term is \\(a=500\\), the common difference is \\(d=100\\), and the number of terms is \\(n=10\\). The tenth-day income is \\(a_{10}=a+(n-1)d=500+9(100)=1400\\). The total can be found by \\(S_n=\\frac{n}{2}[2a+(n-1)d]\\): \\(S_{10}=\\frac{10}{2}[2(500)+9(100)]=5(1900)=9500\\). Option A, ₹9,000, is wrong because it does not add the ten correct terms. Option B, ₹9,250, is wrong because the arithmetic calculation is incomplete or inaccurate. Option C, ₹9,500, is correct. Option D, ₹9,750, is also too high and does not follow the given first term and increase. A quick check is to list the terms: 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300 and 1400; their sum is ₹9,500. Memory cue: identify first term, common difference and number of terms before using the AP sum formula.