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ReasoningAges 16-18

Linear nth-term sequences

Use Tₙ = a + (n − 1)d to find a specific term in a linear arithmetic sequence. Review suitability for your learners before teaching.

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Age band:Ages 13-15Ages 16-18

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Worksheet StudioPractice pack · Ages 16-18

Linear nth-term sequences

Take your time. Show your thinking.

  1. 1. Find the 22th term of the arithmetic sequence 12, 18, 24, 30, ...

    22-1012-1018-1024-10?

  2. 2. Find the 20th term of the arithmetic sequence 11, 13, 15, 17, ...

    20-911-913-915-9?

  3. 3. Find the 15th term of the arithmetic sequence 6, 14, 22, 30, ...

    15-96-914-922-9?

  4. 4. Find the 15th term of the arithmetic sequence 14, 23, 32, 41, ...

    15-114-123-132-1?

  5. 5. Find the 19th term of the arithmetic sequence 17, 23, 29, 35, ...

    19-217-223-229-2?

  6. 6. Find the 20th term of the arithmetic sequence 2, 8, 14, 20, ...

    20-182-188-1814-18?

  7. 7. Find the 22th term of the arithmetic sequence 15, 17, 19, 21, ...

    22-715-717-719-7?

  8. 8. Find the 20th term of the arithmetic sequence 11, 19, 27, 35, ...

    20-911-919-927-9?

  9. 9. Find the 19th term of the arithmetic sequence 18, 23, 28, 33, ...

    19-118-123-128-1?

  10. 10. Find the 23th term of the arithmetic sequence 8, 11, 14, 17, ...

    23-158-1511-1514-15?

  11. 11. Find the 10th term of the arithmetic sequence 20, 27, 34, 41, ...

    10+1020+1027+1034+10?

  12. 12. Find the 23th term of the arithmetic sequence 24, 30, 36, 42, ...

    23+124+130+136+1?
12 questions · Seed 104739 · Age guidance, not curriculum certification
View the answer key
Worksheet StudioAnswer key · Ages 16-18

Linear nth-term sequences

Answers and reasoning. Review before teaching.

  1. 1. Find the 22th term of the arithmetic sequence 12, 18, 24, 30, ...

    138

    First term a = 12 and common difference d = 6. Using a + (n − 1)d gives 12 + 21 × 6 = 138.

  2. 2. Find the 20th term of the arithmetic sequence 11, 13, 15, 17, ...

    49

    First term a = 11 and common difference d = 2. Using a + (n − 1)d gives 11 + 19 × 2 = 49.

  3. 3. Find the 15th term of the arithmetic sequence 6, 14, 22, 30, ...

    118

    First term a = 6 and common difference d = 8. Using a + (n − 1)d gives 6 + 14 × 8 = 118.

  4. 4. Find the 15th term of the arithmetic sequence 14, 23, 32, 41, ...

    140

    First term a = 14 and common difference d = 9. Using a + (n − 1)d gives 14 + 14 × 9 = 140.

  5. 5. Find the 19th term of the arithmetic sequence 17, 23, 29, 35, ...

    125

    First term a = 17 and common difference d = 6. Using a + (n − 1)d gives 17 + 18 × 6 = 125.

  6. 6. Find the 20th term of the arithmetic sequence 2, 8, 14, 20, ...

    116

    First term a = 2 and common difference d = 6. Using a + (n − 1)d gives 2 + 19 × 6 = 116.

  7. 7. Find the 22th term of the arithmetic sequence 15, 17, 19, 21, ...

    57

    First term a = 15 and common difference d = 2. Using a + (n − 1)d gives 15 + 21 × 2 = 57.

  8. 8. Find the 20th term of the arithmetic sequence 11, 19, 27, 35, ...

    163

    First term a = 11 and common difference d = 8. Using a + (n − 1)d gives 11 + 19 × 8 = 163.

  9. 9. Find the 19th term of the arithmetic sequence 18, 23, 28, 33, ...

    108

    First term a = 18 and common difference d = 5. Using a + (n − 1)d gives 18 + 18 × 5 = 108.

  10. 10. Find the 23th term of the arithmetic sequence 8, 11, 14, 17, ...

    74

    First term a = 8 and common difference d = 3. Using a + (n − 1)d gives 8 + 22 × 3 = 74.

  11. 11. Find the 10th term of the arithmetic sequence 20, 27, 34, 41, ...

    83

    First term a = 20 and common difference d = 7. Using a + (n − 1)d gives 20 + 9 × 7 = 83.

  12. 12. Find the 23th term of the arithmetic sequence 24, 30, 36, 42, ...

    156

    First term a = 24 and common difference d = 6. Using a + (n − 1)d gives 24 + 22 × 6 = 156.

12 questions · Seed 104739 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 16-18

Linear nth-term sequences

Take your time. Show your thinking.

  1. 1. Find the 22th term of the arithmetic sequence 12, 18, 24, 30, ...

    22-1012-1018-1024-10?

  2. 2. Find the 20th term of the arithmetic sequence 11, 13, 15, 17, ...

    20-911-913-915-9?

  3. 3. Find the 15th term of the arithmetic sequence 6, 14, 22, 30, ...

    15-96-914-922-9?

  4. 4. Find the 15th term of the arithmetic sequence 14, 23, 32, 41, ...

    15-114-123-132-1?

  5. 5. Find the 19th term of the arithmetic sequence 17, 23, 29, 35, ...

    19-217-223-229-2?

  6. 6. Find the 20th term of the arithmetic sequence 2, 8, 14, 20, ...

    20-182-188-1814-18?

  7. 7. Find the 22th term of the arithmetic sequence 15, 17, 19, 21, ...

    22-715-717-719-7?

  8. 8. Find the 20th term of the arithmetic sequence 11, 19, 27, 35, ...

    20-911-919-927-9?

  9. 9. Find the 19th term of the arithmetic sequence 18, 23, 28, 33, ...

    19-118-123-128-1?

  10. 10. Find the 23th term of the arithmetic sequence 8, 11, 14, 17, ...

    23-158-1511-1514-15?

  11. 11. Find the 10th term of the arithmetic sequence 20, 27, 34, 41, ...

    10+1020+1027+1034+10?

  12. 12. Find the 23th term of the arithmetic sequence 24, 30, 36, 42, ...

    23+124+130+136+1?
12 questions · Seed 104739 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 16-18

Linear nth-term sequences

Answers and reasoning. Review before teaching.

  1. 1. Find the 22th term of the arithmetic sequence 12, 18, 24, 30, ...

    138

    First term a = 12 and common difference d = 6. Using a + (n − 1)d gives 12 + 21 × 6 = 138.

  2. 2. Find the 20th term of the arithmetic sequence 11, 13, 15, 17, ...

    49

    First term a = 11 and common difference d = 2. Using a + (n − 1)d gives 11 + 19 × 2 = 49.

  3. 3. Find the 15th term of the arithmetic sequence 6, 14, 22, 30, ...

    118

    First term a = 6 and common difference d = 8. Using a + (n − 1)d gives 6 + 14 × 8 = 118.

  4. 4. Find the 15th term of the arithmetic sequence 14, 23, 32, 41, ...

    140

    First term a = 14 and common difference d = 9. Using a + (n − 1)d gives 14 + 14 × 9 = 140.

  5. 5. Find the 19th term of the arithmetic sequence 17, 23, 29, 35, ...

    125

    First term a = 17 and common difference d = 6. Using a + (n − 1)d gives 17 + 18 × 6 = 125.

  6. 6. Find the 20th term of the arithmetic sequence 2, 8, 14, 20, ...

    116

    First term a = 2 and common difference d = 6. Using a + (n − 1)d gives 2 + 19 × 6 = 116.

  7. 7. Find the 22th term of the arithmetic sequence 15, 17, 19, 21, ...

    57

    First term a = 15 and common difference d = 2. Using a + (n − 1)d gives 15 + 21 × 2 = 57.

  8. 8. Find the 20th term of the arithmetic sequence 11, 19, 27, 35, ...

    163

    First term a = 11 and common difference d = 8. Using a + (n − 1)d gives 11 + 19 × 8 = 163.

  9. 9. Find the 19th term of the arithmetic sequence 18, 23, 28, 33, ...

    108

    First term a = 18 and common difference d = 5. Using a + (n − 1)d gives 18 + 18 × 5 = 108.

  10. 10. Find the 23th term of the arithmetic sequence 8, 11, 14, 17, ...

    74

    First term a = 8 and common difference d = 3. Using a + (n − 1)d gives 8 + 22 × 3 = 74.

  11. 11. Find the 10th term of the arithmetic sequence 20, 27, 34, 41, ...

    83

    First term a = 20 and common difference d = 7. Using a + (n − 1)d gives 20 + 9 × 7 = 83.

  12. 12. Find the 23th term of the arithmetic sequence 24, 30, 36, 42, ...

    156

    First term a = 24 and common difference d = 6. Using a + (n − 1)d gives 24 + 22 × 6 = 156.

12 questions · Seed 104739 · Age guidance, not curriculum certification