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The nth term of an AP sheet
3-mark answer frame

The 5th term of an AP is 19 and its 12th term is 47. Find the AP and its 25th term.

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

  1. 1 · Write what is given and what is to be found. Given: a₅ = 19 and a₁₂ = 47. To find: a, d, the AP and a₂₅.
  2. 2 · Write the formula or theorem. aₙ = a + (n − 1)d
  3. 3 · Form two equations.
    • a + 4d = 19 ... (1)
    • a + 11d = 47 ... (2)
  4. 4 · Solve them.
    • (2) − (1): 7d = 28, so d = 4
    • From (1): a = 19 − 16 = 3
  5. 5 · Write the AP and the term. The AP is 3, 7, 11, 15, ... and a₂₅ = 3 + 24 × 4 = 99.
  6. 6 · Check and box the answer. Check: a₁₂ = 3 + 11 × 4 = 47. Answer: AP 3, 7, 11, ...; a₂₅ = 99.

Scoring tip: Number your equations (1) and (2) and say which one you subtract. The method earns marks even if the arithmetic slips.