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ReasoningAges 13-15

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 13-15

Linear nth-term sequences

Take your time. Show your thinking.

  1. 1. Find the 19th term of the arithmetic sequence 17, 20, 23, 26, ...

    19-217-220-223-2?

  2. 2. Find the 9th term of the arithmetic sequence 7, 17, 27, 37, ...

    9-27-217-227-2?

  3. 3. Find the 23th term of the arithmetic sequence 19, 26, 33, 40, ...

    23-419-426-433-4?

  4. 4. Find the 11th term of the arithmetic sequence 15, 24, 33, 42, ...

    11+415+424+433+4?

  5. 5. Find the 10th term of the arithmetic sequence 13, 17, 21, 25, ...

    10+313+317+321+3?

  6. 6. Find the 20th term of the arithmetic sequence 5, 16, 27, 38, ...

    20-155-1516-1527-15?

  7. 7. Find the 14th term of the arithmetic sequence 21, 23, 25, 27, ...

    14+721+723+725+7?

  8. 8. Find the 17th term of the arithmetic sequence 8, 17, 26, 35, ...

    17-98-917-926-9?

  9. 9. Find the 18th term of the arithmetic sequence 23, 31, 39, 47, ...

    18+523+531+539+5?

  10. 10. Find the 14th term of the arithmetic sequence 10, 19, 28, 37, ...

    14-410-419-428-4?

  11. 11. Find the 22th term of the arithmetic sequence 25, 27, 29, 31, ...

    22+325+327+329+3?

  12. 12. Find the 22th term of the arithmetic sequence 3, 12, 21, 30, ...

    22-193-1912-1921-19?
12 questions · Seed 61 · Age guidance, not curriculum certification
View the answer key
Worksheet StudioAnswer key · Ages 13-15

Linear nth-term sequences

Answers and reasoning. Review before teaching.

  1. 1. Find the 19th term of the arithmetic sequence 17, 20, 23, 26, ...

    71

    First term a = 17 and common difference d = 3. Using a + (n − 1)d gives 17 + 18 × 3 = 71.

  2. 2. Find the 9th term of the arithmetic sequence 7, 17, 27, 37, ...

    87

    First term a = 7 and common difference d = 10. Using a + (n − 1)d gives 7 + 8 × 10 = 87.

  3. 3. Find the 23th term of the arithmetic sequence 19, 26, 33, 40, ...

    173

    First term a = 19 and common difference d = 7. Using a + (n − 1)d gives 19 + 22 × 7 = 173.

  4. 4. Find the 11th term of the arithmetic sequence 15, 24, 33, 42, ...

    105

    First term a = 15 and common difference d = 9. Using a + (n − 1)d gives 15 + 10 × 9 = 105.

  5. 5. Find the 10th term of the arithmetic sequence 13, 17, 21, 25, ...

    49

    First term a = 13 and common difference d = 4. Using a + (n − 1)d gives 13 + 9 × 4 = 49.

  6. 6. Find the 20th term of the arithmetic sequence 5, 16, 27, 38, ...

    214

    First term a = 5 and common difference d = 11. Using a + (n − 1)d gives 5 + 19 × 11 = 214.

  7. 7. Find the 14th term of the arithmetic sequence 21, 23, 25, 27, ...

    47

    First term a = 21 and common difference d = 2. Using a + (n − 1)d gives 21 + 13 × 2 = 47.

  8. 8. Find the 17th term of the arithmetic sequence 8, 17, 26, 35, ...

    152

    First term a = 8 and common difference d = 9. Using a + (n − 1)d gives 8 + 16 × 9 = 152.

  9. 9. Find the 18th term of the arithmetic sequence 23, 31, 39, 47, ...

    159

    First term a = 23 and common difference d = 8. Using a + (n − 1)d gives 23 + 17 × 8 = 159.

  10. 10. Find the 14th term of the arithmetic sequence 10, 19, 28, 37, ...

    127

    First term a = 10 and common difference d = 9. Using a + (n − 1)d gives 10 + 13 × 9 = 127.

  11. 11. Find the 22th term of the arithmetic sequence 25, 27, 29, 31, ...

    67

    First term a = 25 and common difference d = 2. Using a + (n − 1)d gives 25 + 21 × 2 = 67.

  12. 12. Find the 22th term of the arithmetic sequence 3, 12, 21, 30, ...

    192

    First term a = 3 and common difference d = 9. Using a + (n − 1)d gives 3 + 21 × 9 = 192.

12 questions · Seed 61 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 13-15

Linear nth-term sequences

Take your time. Show your thinking.

  1. 1. Find the 19th term of the arithmetic sequence 17, 20, 23, 26, ...

    19-217-220-223-2?

  2. 2. Find the 9th term of the arithmetic sequence 7, 17, 27, 37, ...

    9-27-217-227-2?

  3. 3. Find the 23th term of the arithmetic sequence 19, 26, 33, 40, ...

    23-419-426-433-4?

  4. 4. Find the 11th term of the arithmetic sequence 15, 24, 33, 42, ...

    11+415+424+433+4?

  5. 5. Find the 10th term of the arithmetic sequence 13, 17, 21, 25, ...

    10+313+317+321+3?

  6. 6. Find the 20th term of the arithmetic sequence 5, 16, 27, 38, ...

    20-155-1516-1527-15?

  7. 7. Find the 14th term of the arithmetic sequence 21, 23, 25, 27, ...

    14+721+723+725+7?

  8. 8. Find the 17th term of the arithmetic sequence 8, 17, 26, 35, ...

    17-98-917-926-9?

  9. 9. Find the 18th term of the arithmetic sequence 23, 31, 39, 47, ...

    18+523+531+539+5?

  10. 10. Find the 14th term of the arithmetic sequence 10, 19, 28, 37, ...

    14-410-419-428-4?

  11. 11. Find the 22th term of the arithmetic sequence 25, 27, 29, 31, ...

    22+325+327+329+3?

  12. 12. Find the 22th term of the arithmetic sequence 3, 12, 21, 30, ...

    22-193-1912-1921-19?
12 questions · Seed 61 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 13-15

Linear nth-term sequences

Answers and reasoning. Review before teaching.

  1. 1. Find the 19th term of the arithmetic sequence 17, 20, 23, 26, ...

    71

    First term a = 17 and common difference d = 3. Using a + (n − 1)d gives 17 + 18 × 3 = 71.

  2. 2. Find the 9th term of the arithmetic sequence 7, 17, 27, 37, ...

    87

    First term a = 7 and common difference d = 10. Using a + (n − 1)d gives 7 + 8 × 10 = 87.

  3. 3. Find the 23th term of the arithmetic sequence 19, 26, 33, 40, ...

    173

    First term a = 19 and common difference d = 7. Using a + (n − 1)d gives 19 + 22 × 7 = 173.

  4. 4. Find the 11th term of the arithmetic sequence 15, 24, 33, 42, ...

    105

    First term a = 15 and common difference d = 9. Using a + (n − 1)d gives 15 + 10 × 9 = 105.

  5. 5. Find the 10th term of the arithmetic sequence 13, 17, 21, 25, ...

    49

    First term a = 13 and common difference d = 4. Using a + (n − 1)d gives 13 + 9 × 4 = 49.

  6. 6. Find the 20th term of the arithmetic sequence 5, 16, 27, 38, ...

    214

    First term a = 5 and common difference d = 11. Using a + (n − 1)d gives 5 + 19 × 11 = 214.

  7. 7. Find the 14th term of the arithmetic sequence 21, 23, 25, 27, ...

    47

    First term a = 21 and common difference d = 2. Using a + (n − 1)d gives 21 + 13 × 2 = 47.

  8. 8. Find the 17th term of the arithmetic sequence 8, 17, 26, 35, ...

    152

    First term a = 8 and common difference d = 9. Using a + (n − 1)d gives 8 + 16 × 9 = 152.

  9. 9. Find the 18th term of the arithmetic sequence 23, 31, 39, 47, ...

    159

    First term a = 23 and common difference d = 8. Using a + (n − 1)d gives 23 + 17 × 8 = 159.

  10. 10. Find the 14th term of the arithmetic sequence 10, 19, 28, 37, ...

    127

    First term a = 10 and common difference d = 9. Using a + (n − 1)d gives 10 + 13 × 9 = 127.

  11. 11. Find the 22th term of the arithmetic sequence 25, 27, 29, 31, ...

    67

    First term a = 25 and common difference d = 2. Using a + (n − 1)d gives 25 + 21 × 2 = 67.

  12. 12. Find the 22th term of the arithmetic sequence 3, 12, 21, 30, ...

    192

    First term a = 3 and common difference d = 9. Using a + (n − 1)d gives 3 + 21 × 9 = 192.

12 questions · Seed 61 · Age guidance, not curriculum certification