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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 23th term of the arithmetic sequence 19, 25, 31, 37, ...

    23-419-425-431-4?

  2. 2. Find the 14th term of the arithmetic sequence 13, 18, 23, 28, ...

    14-113-118-123-1?

  3. 3. Find the 8th term of the arithmetic sequence 23, 27, 31, 35, ...

    8+1523+1527+1531+15?

  4. 4. Find the 8th term of the arithmetic sequence 8, 18, 28, 38, ...

    8+08+018+028+0?

  5. 5. Find the 25th term of the arithmetic sequence 17, 23, 29, 35, ...

    25-817-823-829-8?

  6. 6. Find the 8th term of the arithmetic sequence 12, 18, 24, 30, ...

    8+412+418+424+4?

  7. 7. Find the 24th term of the arithmetic sequence 5, 16, 27, 38, ...

    24-195-1916-1927-19?

  8. 8. Find the 10th term of the arithmetic sequence 20, 30, 40, 50, ...

    10+1020+1030+1040+10?

  9. 9. Find the 17th term of the arithmetic sequence 6, 13, 20, 27, ...

    17-116-1113-1120-11?

  10. 10. Find the 11th term of the arithmetic sequence 6, 17, 28, 39, ...

    11-56-517-528-5?

  11. 11. Find the 23th term of the arithmetic sequence 17, 28, 39, 50, ...

    23-617-628-639-6?

  12. 12. Find the 11th term of the arithmetic sequence 22, 30, 38, 46, ...

    11+1122+1130+1138+11?
12 questions · Seed 104743 · 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 23th term of the arithmetic sequence 19, 25, 31, 37, ...

    151

    First term a = 19 and common difference d = 6. Using a + (n − 1)d gives 19 + 22 × 6 = 151.

  2. 2. Find the 14th term of the arithmetic sequence 13, 18, 23, 28, ...

    78

    First term a = 13 and common difference d = 5. Using a + (n − 1)d gives 13 + 13 × 5 = 78.

  3. 3. Find the 8th term of the arithmetic sequence 23, 27, 31, 35, ...

    51

    First term a = 23 and common difference d = 4. Using a + (n − 1)d gives 23 + 7 × 4 = 51.

  4. 4. Find the 8th term of the arithmetic sequence 8, 18, 28, 38, ...

    78

    First term a = 8 and common difference d = 10. Using a + (n − 1)d gives 8 + 7 × 10 = 78.

  5. 5. Find the 25th term of the arithmetic sequence 17, 23, 29, 35, ...

    161

    First term a = 17 and common difference d = 6. Using a + (n − 1)d gives 17 + 24 × 6 = 161.

  6. 6. Find the 8th term of the arithmetic sequence 12, 18, 24, 30, ...

    54

    First term a = 12 and common difference d = 6. Using a + (n − 1)d gives 12 + 7 × 6 = 54.

  7. 7. Find the 24th term of the arithmetic sequence 5, 16, 27, 38, ...

    258

    First term a = 5 and common difference d = 11. Using a + (n − 1)d gives 5 + 23 × 11 = 258.

  8. 8. Find the 10th term of the arithmetic sequence 20, 30, 40, 50, ...

    110

    First term a = 20 and common difference d = 10. Using a + (n − 1)d gives 20 + 9 × 10 = 110.

  9. 9. Find the 17th term of the arithmetic sequence 6, 13, 20, 27, ...

    118

    First term a = 6 and common difference d = 7. Using a + (n − 1)d gives 6 + 16 × 7 = 118.

  10. 10. Find the 11th term of the arithmetic sequence 6, 17, 28, 39, ...

    116

    First term a = 6 and common difference d = 11. Using a + (n − 1)d gives 6 + 10 × 11 = 116.

  11. 11. Find the 23th term of the arithmetic sequence 17, 28, 39, 50, ...

    259

    First term a = 17 and common difference d = 11. Using a + (n − 1)d gives 17 + 22 × 11 = 259.

  12. 12. Find the 11th term of the arithmetic sequence 22, 30, 38, 46, ...

    102

    First term a = 22 and common difference d = 8. Using a + (n − 1)d gives 22 + 10 × 8 = 102.

12 questions · Seed 104743 · 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 23th term of the arithmetic sequence 19, 25, 31, 37, ...

    23-419-425-431-4?

  2. 2. Find the 14th term of the arithmetic sequence 13, 18, 23, 28, ...

    14-113-118-123-1?

  3. 3. Find the 8th term of the arithmetic sequence 23, 27, 31, 35, ...

    8+1523+1527+1531+15?

  4. 4. Find the 8th term of the arithmetic sequence 8, 18, 28, 38, ...

    8+08+018+028+0?

  5. 5. Find the 25th term of the arithmetic sequence 17, 23, 29, 35, ...

    25-817-823-829-8?

  6. 6. Find the 8th term of the arithmetic sequence 12, 18, 24, 30, ...

    8+412+418+424+4?

  7. 7. Find the 24th term of the arithmetic sequence 5, 16, 27, 38, ...

    24-195-1916-1927-19?

  8. 8. Find the 10th term of the arithmetic sequence 20, 30, 40, 50, ...

    10+1020+1030+1040+10?

  9. 9. Find the 17th term of the arithmetic sequence 6, 13, 20, 27, ...

    17-116-1113-1120-11?

  10. 10. Find the 11th term of the arithmetic sequence 6, 17, 28, 39, ...

    11-56-517-528-5?

  11. 11. Find the 23th term of the arithmetic sequence 17, 28, 39, 50, ...

    23-617-628-639-6?

  12. 12. Find the 11th term of the arithmetic sequence 22, 30, 38, 46, ...

    11+1122+1130+1138+11?
12 questions · Seed 104743 · 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 23th term of the arithmetic sequence 19, 25, 31, 37, ...

    151

    First term a = 19 and common difference d = 6. Using a + (n − 1)d gives 19 + 22 × 6 = 151.

  2. 2. Find the 14th term of the arithmetic sequence 13, 18, 23, 28, ...

    78

    First term a = 13 and common difference d = 5. Using a + (n − 1)d gives 13 + 13 × 5 = 78.

  3. 3. Find the 8th term of the arithmetic sequence 23, 27, 31, 35, ...

    51

    First term a = 23 and common difference d = 4. Using a + (n − 1)d gives 23 + 7 × 4 = 51.

  4. 4. Find the 8th term of the arithmetic sequence 8, 18, 28, 38, ...

    78

    First term a = 8 and common difference d = 10. Using a + (n − 1)d gives 8 + 7 × 10 = 78.

  5. 5. Find the 25th term of the arithmetic sequence 17, 23, 29, 35, ...

    161

    First term a = 17 and common difference d = 6. Using a + (n − 1)d gives 17 + 24 × 6 = 161.

  6. 6. Find the 8th term of the arithmetic sequence 12, 18, 24, 30, ...

    54

    First term a = 12 and common difference d = 6. Using a + (n − 1)d gives 12 + 7 × 6 = 54.

  7. 7. Find the 24th term of the arithmetic sequence 5, 16, 27, 38, ...

    258

    First term a = 5 and common difference d = 11. Using a + (n − 1)d gives 5 + 23 × 11 = 258.

  8. 8. Find the 10th term of the arithmetic sequence 20, 30, 40, 50, ...

    110

    First term a = 20 and common difference d = 10. Using a + (n − 1)d gives 20 + 9 × 10 = 110.

  9. 9. Find the 17th term of the arithmetic sequence 6, 13, 20, 27, ...

    118

    First term a = 6 and common difference d = 7. Using a + (n − 1)d gives 6 + 16 × 7 = 118.

  10. 10. Find the 11th term of the arithmetic sequence 6, 17, 28, 39, ...

    116

    First term a = 6 and common difference d = 11. Using a + (n − 1)d gives 6 + 10 × 11 = 116.

  11. 11. Find the 23th term of the arithmetic sequence 17, 28, 39, 50, ...

    259

    First term a = 17 and common difference d = 11. Using a + (n − 1)d gives 17 + 22 × 11 = 259.

  12. 12. Find the 11th term of the arithmetic sequence 22, 30, 38, 46, ...

    102

    First term a = 22 and common difference d = 8. Using a + (n − 1)d gives 22 + 10 × 8 = 102.

12 questions · Seed 104743 · Age guidance, not curriculum certification