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Arithmetic progressions (AP) sheet
Essay frame

A clerk starts on Rs. 60,000 a month with a Rs. 2,500 increment each year. Find (a) the monthly salary in year 10, (b) the total earned in 10 years, (c) the first year in which the monthly salary exceeds Rs. 85,000.

How to lay out the answer. Follow the frame, then write it in your own words.

  1. 1 · Identify the AP. a = 60,000, d = 2,500 (monthly rates by year).
  2. 2 · (a) nth term. T10 = 60,000 + 9 × 2,500 = Rs. 82,500.
  3. 3 · (b) Sum of the rates. S10 = 10/2 (60,000 + 82,500) = 712,500.
  4. 4 · Convert to money earned. Each rate is paid 12 times: 12 × 712,500 = Rs. 8,550,000.
  5. 5 · (c) Set up an inequality. 60,000 + (n − 1) × 2,500 > 85,000, so (n − 1) > 10 and n > 11.
  6. 6 · Interpret. Year 11 pays exactly Rs. 85,000; year 12 is the first above it (Rs. 87,500).
  7. 7 · Business link. HR uses the same sums to budget a salary scale for every staff grade.