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Form 5 Sequences Practice

Form 5 · 40 practice questions with instant marking and worked solutions.

Sequences is an important part of the Form 5 mathematics curriculum. This topic develops terms, indices, general terms, arithmetic and geometric structure. Begin by identifying what every number, symbol, diagram and unit represents. Translate the information into a mathematical relationship before calculating. Each line of working should have a purpose. Finally use estimation, substitution, an inverse operation, or a second representation to check the result. This habit separates a misunderstanding from a copying error and makes correction more useful.

A reliable approach to Sequences has four stages. First, mark the given information and the quantity required. Second, choose an appropriate representation, property or formula. Third, carry out the operations in a clear order while retaining signs and units. Fourth, return to the original context and decide whether the result is possible. For a graph or table, read the title, scale and labels before using a value. For algebra, inspect brackets, negative signs and the order of operations before simplifying.

The forty original questions in this topic use a shared mathematical specification in Chinese and English. Difficulty rises from level 1 to level 5. Early questions establish the language and direct skills of Sequences; middle questions add two-step reasoning, conversions and common variations; later questions connect ideas and require a deliberate check. In multiple-choice work, calculate before looking at the choices. In fill-in and short-answer work, retain decisive steps. For true-or-false statements, support the decision with a calculation or counterexample. Four of them are DSE Paper 1 style structured questions answered in parts (a), (b), (c), where later parts build on earlier ones.

Effective revision is more than recording a score. After completing the Sequences set, group errors by concept tags and decide whether each problem arose from interpretation, forming an expression, calculation, or presenting the answer. Retry the item on a later day without opening the solution, then test the same method with a different value. If the same tag appears repeatedly, return to the explanation and rebuild the concept. If signs or units are the issue, use a fixed pre-submission checklist.

Sequences should also connect with the rest of mathematics. Number and algebra supply calculation tools; measurement and geometry give spatial meaning; data handling asks what a result means. A learner who can explain aloud why every step is valid has moved beyond imitation. Estimate a reasonable range, complete an exact solution, and compare the two. Agreement between context, estimate and exact answer is strong evidence that the solution is sound.

Start practising

  1. 1 Basic
    In Sequences, calculate $a_1=7,\ d=3,\ n=5$. Choose the correct answer.
  2. 2 Basic
    In Sequences, calculate $a_1=8,\ d=4,\ n=6$. Give the numerical value only.

  3. 3 Basic
    In Sequences, calculate $a_1=9,\ d=5,\ n=7$. Show the essential working and give the numerical value.

  4. 4 Basic
    In Sequences, the value of $a_1=6,\ d=6,\ n=8$ is 49. Is this statement true?
  5. 5 Basic
    An arithmetic sequence has first term $-2$ and common difference $2$. Find the 19th term. Choose the correct answer.
  6. 6 Basic
    An arithmetic sequence has first term $6$ and common difference $2$. Find the sum of the first 16 terms. Give the answer only.

  7. 7 Basic
    A geometric sequence has first term $1$ and common ratio $3$. Find the 7th term. Show the essential working and give the answer.

  8. 8 Basic
    A geometric sequence has first term $3$ and common ratio $2$. The sum of the first 6 terms is 96. Is this true?
  9. 9 Standard
    In Sequences, calculate $a_1=11,\ d=2,\ n=9$. Choose the correct answer.
  10. 10 Standard
    In Sequences, calculate $a_1=12,\ d=3,\ n=4$. Give the numerical value only.

  11. 11 Standard
    In Sequences, calculate $a_1=13,\ d=4,\ n=5$. Show the essential working and give the numerical value.

  12. 12 Standard
    In Sequences, the value of $a_1=10,\ d=5,\ n=6$ is 35. Is this statement true?
  13. 13 Standard
    An infinite geometric series has first term $3$ and common ratio $\frac{3}{4}$. Find the sum to infinity. Choose the correct answer.
  14. 14 Standard
    The $n$th term of the arithmetic sequence $0, 5, 10, \dots$ is $145$. Find the value of $n$. Give the answer only.

  15. 15 Standard
    The 4th term of an arithmetic sequence is $3$ and the 7th term is $6$. Find the common difference. Show the essential working and give the answer.

  16. 16 Standard DSE long question
    An arithmetic sequence has first term $8$ and fifth term $24$. Answer each part; give the answer only.
    1. (a) Find the common difference.
    2. (b) Find the 11th term.
    3. (c) Find the sum of the first 11 terms.
  17. 17 Advanced
    In Sequences, calculate $a_1=15,\ d=6,\ n=7$. Choose the correct answer.
  18. 18 Advanced
    In Sequences, calculate $a_1=16,\ d=2,\ n=8$. Give the numerical value only.

  19. 19 Advanced
    In Sequences, calculate $a_1=17,\ d=3,\ n=9$. Show the essential working and give the numerical value.

  20. 20 Advanced
    In Sequences, the value of $a_1=14,\ d=4,\ n=4$ is 27. Is this statement true?
  21. 21 Advanced
    An arithmetic sequence has first term $-2$ and common difference $-6$. Find the 31st term. Choose the correct answer.
  22. 22 Advanced
    An arithmetic sequence has first term $4$ and common difference $5$. Find the sum of the first 23 terms. Give the answer only.

  23. 23 Advanced
    A geometric sequence has first term $4$ and common ratio $\frac{1}{2}$. The 7th term is 1/16. Is this true?
  24. 24 Advanced DSE long question
    A geometric sequence has first term $16$ and common ratio $\frac{1}{3}$. Answer each part; give the answer only.
    1. (a) Find the 4th term (as a fraction in lowest terms).
    2. (b) Find the sum of the first 4 terms (as a fraction in lowest terms).
    3. (c) Find the sum to infinity.
  25. 25 Challenging
    In Sequences, calculate $a_1=19,\ d=5,\ n=5$. Choose the correct answer.
  26. 26 Challenging
    In Sequences, calculate $a_1=20,\ d=6,\ n=6$. Give the numerical value only.

  27. 27 Challenging
    In Sequences, calculate $a_1=21,\ d=2,\ n=7$. Show the essential working and give the numerical value.

  28. 28 Challenging
    In Sequences, the value of $a_1=18,\ d=3,\ n=8$ is 39. Is this statement true?
  29. 29 Challenging
    A geometric sequence has first term $1$ and common ratio $2$. Find the sum of the first 6 terms. Choose the correct answer.
  30. 30 Challenging
    An infinite geometric series has first term $3$ and common ratio $-\frac{1}{2}$. Find the sum to infinity. Show the essential working and give the answer.

  31. 31 Challenging
    The $n$th term of the arithmetic sequence $8, 12, 16, \dots$ is $144$. The value of $n$ is 34. Is this true?
  32. 32 Challenging DSE long question
    An arithmetic sequence has first term $-6$ and fifth term $2$. Answer each part; give the answer only.
    1. (a) Find the common difference.
    2. (b) Find the 19th term.
    3. (c) Find the sum of the first 19 terms.
  33. 33 Elite
    In Sequences, calculate $a_1=23,\ d=4,\ n=9$. Choose the correct answer.
  34. 34 Elite
    In Sequences, calculate $a_1=24,\ d=5,\ n=4$. Give the numerical value only.

  35. 35 Elite
    In Sequences, calculate $a_1=25,\ d=6,\ n=5$. Show the essential working and give the numerical value.

  36. 36 Elite
    In Sequences, the value of $a_1=22,\ d=2,\ n=6$ is 33. Is this statement true?
  37. 37 Elite
    The 2nd term of an arithmetic sequence is $6$ and the 11th term is $-30$. Find the common difference. Give the answer only.

  38. 38 Elite
    An arithmetic sequence has first term $7$ and common difference $-2$. Find the 21st term. Show the essential working and give the answer.

  39. 39 Elite
    An arithmetic sequence has first term $2$ and common difference $-3$. The sum of the first 35 terms is -1715. Is this true?
  40. 40 Elite DSE long question
    A geometric sequence has first term $16$ and common ratio $-\frac{1}{2}$. Answer each part; give the answer only.
    1. (a) Find the 4th term.
    2. (b) Find the sum of the first 4 terms.
    3. (c) Find the sum to infinity (as a fraction in lowest terms).

The report lists what you got wrong and why. Only you can see it.

Common mistakes

Common mistakes in Sequences

This topic needs particular care with terms, indices, general terms, arithmetic and geometric structure. The first mistake is applying a remembered rule before reading all conditions. The second is compressing working so much that a sign, bracket, decimal point or unit disappears. The third is accepting an impossible answer without checking: for example, a probability above one, a negative physical length, an angle outside the geometric constraints, or a result far from the estimate. Separate the conditions, model, calculation and check, and finish by stating what the answer represents.

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