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IGCSE Maths · Edexcel 4XMA1 · Unit 2 Higher · Sequences

Arithmetic Sequences and Series — Practice Questions

12 exam-style questions (37 marks), building from warm-up to grade 8–9. Show full working: Edexcel gives method marks even when the final answer is wrong.

Section A — Warm-up (grades 5–6)
  1. (2 marks)For the sequence 5, 9, 13, 17, …
    (a) find an expression for the nth term
    (b) find the 30th term.
  2. (2 marks)An arithmetic sequence has first term 20 and common difference −3. Find the 15th term.
  3. (2 marks)Is 150 a term of the sequence 4, 11, 18, 25, …? Show how you decide.
  4. (2 marks)Find the sum of the integers from 1 to 100.
Section B — Core (grades 6–7)
  1. (3 marks)Find the sum of the first 25 terms of the series 2 + 5 + 8 + …
  2. (3 marks)Find the sum 6 + 10 + 14 + … + 86.
  3. (4 marks)The 3rd term of an arithmetic sequence is 11 and the 8th term is 31. Find the sum of the first 15 terms.
  4. (4 marks)Maya saves $500 in month 1, and each month she saves $150 more than the month before.
    (a) How much does she save in month 12?
    (b) What is the total she has saved after 12 months?
Section C — Stretch (grades 8–9)
  1. (4 marks)How many terms of the series 3 + 7 + 11 + … are needed for the sum to be 465?
  2. (4 marks)Find the sum of all the multiples of 7 between 100 and 300.
    HintFind the first and last multiples of 7 in the range.
  3. (3 marks)Prove that the sum of the first n odd numbers is n².
  4. (4 marks)The sum of the first n terms of an arithmetic series is Sn = 3n² + 2n. Find the first term and the common difference.
    HintS1 is the first term. S2 − S1 is the second term.
When you’re doneRevise the method in the notes, then mark your answers with the worked solutions.
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