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Sum of an arithmetic series sheet
5-mark answer frame

A word problem on the sum of an AP (seats, savings or stacks): find the total.

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. Identify a, d and n from the story.
  2. 2 · Show that the data form an AP. Write the first few terms, e.g. 25, 28, 31, ..., and state d.
  3. 3 · Write the formula or theorem. Sₙ = (n/2)[2a + (n − 1)d].
  4. 4 · Substitute the values. S₂₀ = (20/2)[2 × 25 + 19 × 3].
  5. 5 · Simplify. = 10 × (50 + 57) = 10 × 107 = 1070.
  6. 6 · Check and box the answer. Check with Sₙ = (n/2)(a + l), and write the unit: seats, ₹ or logs.

Scoring tip: In word problems, write 'a = ..., d = ..., n = ...' on one line before the formula. It earns a mark even if you slip later.