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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 9th term of the arithmetic sequence 3, 9, 15, 21, ...

    9-63-69-615-6?

  2. 2. Find the 17th term of the arithmetic sequence 2, 5, 8, 11, ...

    17-152-155-158-15?

  3. 3. Find the 10th term of the arithmetic sequence 22, 26, 30, 34, ...

    10+1222+1226+1230+12?

  4. 4. Find the 24th term of the arithmetic sequence 4, 6, 8, 10, ...

    24-204-206-208-20?

  5. 5. Find the 10th term of the arithmetic sequence 19, 21, 23, 25, ...

    10+919+921+923+9?

  6. 6. Find the 15th term of the arithmetic sequence 7, 17, 27, 37, ...

    15-87-817-827-8?

  7. 7. Find the 19th term of the arithmetic sequence 14, 22, 30, 38, ...

    19-514-522-530-5?

  8. 8. Find the 20th term of the arithmetic sequence 12, 19, 26, 33, ...

    20-812-819-826-8?

  9. 9. Find the 16th term of the arithmetic sequence 9, 11, 13, 15, ...

    16-79-711-713-7?

  10. 10. Find the 11th term of the arithmetic sequence 2, 9, 16, 23, ...

    11-92-99-916-9?

  11. 11. Find the 11th term of the arithmetic sequence 16, 21, 26, 31, ...

    11+516+521+526+5?

  12. 12. Find the 10th term of the arithmetic sequence 9, 16, 23, 30, ...

    10-19-116-123-1?
12 questions · Seed 44 · 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 9th term of the arithmetic sequence 3, 9, 15, 21, ...

    51

    First term a = 3 and common difference d = 6. Using a + (n − 1)d gives 3 + 8 × 6 = 51.

  2. 2. Find the 17th term of the arithmetic sequence 2, 5, 8, 11, ...

    50

    First term a = 2 and common difference d = 3. Using a + (n − 1)d gives 2 + 16 × 3 = 50.

  3. 3. Find the 10th term of the arithmetic sequence 22, 26, 30, 34, ...

    58

    First term a = 22 and common difference d = 4. Using a + (n − 1)d gives 22 + 9 × 4 = 58.

  4. 4. Find the 24th term of the arithmetic sequence 4, 6, 8, 10, ...

    50

    First term a = 4 and common difference d = 2. Using a + (n − 1)d gives 4 + 23 × 2 = 50.

  5. 5. Find the 10th term of the arithmetic sequence 19, 21, 23, 25, ...

    37

    First term a = 19 and common difference d = 2. Using a + (n − 1)d gives 19 + 9 × 2 = 37.

  6. 6. Find the 15th term of the arithmetic sequence 7, 17, 27, 37, ...

    147

    First term a = 7 and common difference d = 10. Using a + (n − 1)d gives 7 + 14 × 10 = 147.

  7. 7. Find the 19th term of the arithmetic sequence 14, 22, 30, 38, ...

    158

    First term a = 14 and common difference d = 8. Using a + (n − 1)d gives 14 + 18 × 8 = 158.

  8. 8. Find the 20th term of the arithmetic sequence 12, 19, 26, 33, ...

    145

    First term a = 12 and common difference d = 7. Using a + (n − 1)d gives 12 + 19 × 7 = 145.

  9. 9. Find the 16th term of the arithmetic sequence 9, 11, 13, 15, ...

    39

    First term a = 9 and common difference d = 2. Using a + (n − 1)d gives 9 + 15 × 2 = 39.

  10. 10. Find the 11th term of the arithmetic sequence 2, 9, 16, 23, ...

    72

    First term a = 2 and common difference d = 7. Using a + (n − 1)d gives 2 + 10 × 7 = 72.

  11. 11. Find the 11th term of the arithmetic sequence 16, 21, 26, 31, ...

    66

    First term a = 16 and common difference d = 5. Using a + (n − 1)d gives 16 + 10 × 5 = 66.

  12. 12. Find the 10th term of the arithmetic sequence 9, 16, 23, 30, ...

    72

    First term a = 9 and common difference d = 7. Using a + (n − 1)d gives 9 + 9 × 7 = 72.

12 questions · Seed 44 · 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 9th term of the arithmetic sequence 3, 9, 15, 21, ...

    9-63-69-615-6?

  2. 2. Find the 17th term of the arithmetic sequence 2, 5, 8, 11, ...

    17-152-155-158-15?

  3. 3. Find the 10th term of the arithmetic sequence 22, 26, 30, 34, ...

    10+1222+1226+1230+12?

  4. 4. Find the 24th term of the arithmetic sequence 4, 6, 8, 10, ...

    24-204-206-208-20?

  5. 5. Find the 10th term of the arithmetic sequence 19, 21, 23, 25, ...

    10+919+921+923+9?

  6. 6. Find the 15th term of the arithmetic sequence 7, 17, 27, 37, ...

    15-87-817-827-8?

  7. 7. Find the 19th term of the arithmetic sequence 14, 22, 30, 38, ...

    19-514-522-530-5?

  8. 8. Find the 20th term of the arithmetic sequence 12, 19, 26, 33, ...

    20-812-819-826-8?

  9. 9. Find the 16th term of the arithmetic sequence 9, 11, 13, 15, ...

    16-79-711-713-7?

  10. 10. Find the 11th term of the arithmetic sequence 2, 9, 16, 23, ...

    11-92-99-916-9?

  11. 11. Find the 11th term of the arithmetic sequence 16, 21, 26, 31, ...

    11+516+521+526+5?

  12. 12. Find the 10th term of the arithmetic sequence 9, 16, 23, 30, ...

    10-19-116-123-1?
12 questions · Seed 44 · 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 9th term of the arithmetic sequence 3, 9, 15, 21, ...

    51

    First term a = 3 and common difference d = 6. Using a + (n − 1)d gives 3 + 8 × 6 = 51.

  2. 2. Find the 17th term of the arithmetic sequence 2, 5, 8, 11, ...

    50

    First term a = 2 and common difference d = 3. Using a + (n − 1)d gives 2 + 16 × 3 = 50.

  3. 3. Find the 10th term of the arithmetic sequence 22, 26, 30, 34, ...

    58

    First term a = 22 and common difference d = 4. Using a + (n − 1)d gives 22 + 9 × 4 = 58.

  4. 4. Find the 24th term of the arithmetic sequence 4, 6, 8, 10, ...

    50

    First term a = 4 and common difference d = 2. Using a + (n − 1)d gives 4 + 23 × 2 = 50.

  5. 5. Find the 10th term of the arithmetic sequence 19, 21, 23, 25, ...

    37

    First term a = 19 and common difference d = 2. Using a + (n − 1)d gives 19 + 9 × 2 = 37.

  6. 6. Find the 15th term of the arithmetic sequence 7, 17, 27, 37, ...

    147

    First term a = 7 and common difference d = 10. Using a + (n − 1)d gives 7 + 14 × 10 = 147.

  7. 7. Find the 19th term of the arithmetic sequence 14, 22, 30, 38, ...

    158

    First term a = 14 and common difference d = 8. Using a + (n − 1)d gives 14 + 18 × 8 = 158.

  8. 8. Find the 20th term of the arithmetic sequence 12, 19, 26, 33, ...

    145

    First term a = 12 and common difference d = 7. Using a + (n − 1)d gives 12 + 19 × 7 = 145.

  9. 9. Find the 16th term of the arithmetic sequence 9, 11, 13, 15, ...

    39

    First term a = 9 and common difference d = 2. Using a + (n − 1)d gives 9 + 15 × 2 = 39.

  10. 10. Find the 11th term of the arithmetic sequence 2, 9, 16, 23, ...

    72

    First term a = 2 and common difference d = 7. Using a + (n − 1)d gives 2 + 10 × 7 = 72.

  11. 11. Find the 11th term of the arithmetic sequence 16, 21, 26, 31, ...

    66

    First term a = 16 and common difference d = 5. Using a + (n − 1)d gives 16 + 10 × 5 = 66.

  12. 12. Find the 10th term of the arithmetic sequence 9, 16, 23, 30, ...

    72

    First term a = 9 and common difference d = 7. Using a + (n − 1)d gives 9 + 9 × 7 = 72.

12 questions · Seed 44 · Age guidance, not curriculum certification