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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 11th term of the arithmetic sequence 14, 19, 24, 29, ...

    11+314+319+324+3?

  2. 2. Find the 12th term of the arithmetic sequence 18, 20, 22, 24, ...

    12+618+620+622+6?

  3. 3. Find the 14th term of the arithmetic sequence 13, 23, 33, 43, ...

    14-113-123-133-1?

  4. 4. Find the 22th term of the arithmetic sequence 9, 14, 19, 24, ...

    22-139-1314-1319-13?

  5. 5. Find the 25th term of the arithmetic sequence 6, 18, 30, 42, ...

    25-196-1918-1930-19?

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

    12-93-912-921-9?

  7. 7. Find the 22th term of the arithmetic sequence 20, 22, 24, 26, ...

    22-220-222-224-2?

  8. 8. Find the 15th term of the arithmetic sequence 5, 17, 29, 41, ...

    15-105-1017-1029-10?

  9. 9. Find the 12th term of the arithmetic sequence 25, 36, 47, 58, ...

    12+1325+1336+1347+13?

  10. 10. Find the 12th term of the arithmetic sequence 15, 27, 39, 51, ...

    12+315+327+339+3?

  11. 11. Find the 25th term of the arithmetic sequence 12, 24, 36, 48, ...

    25-1312-1324-1336-13?

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

    8+1523+1527+1531+15?
12 questions · Seed 45 · 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 11th term of the arithmetic sequence 14, 19, 24, 29, ...

    64

    First term a = 14 and common difference d = 5. Using a + (n − 1)d gives 14 + 10 × 5 = 64.

  2. 2. Find the 12th term of the arithmetic sequence 18, 20, 22, 24, ...

    40

    First term a = 18 and common difference d = 2. Using a + (n − 1)d gives 18 + 11 × 2 = 40.

  3. 3. Find the 14th term of the arithmetic sequence 13, 23, 33, 43, ...

    143

    First term a = 13 and common difference d = 10. Using a + (n − 1)d gives 13 + 13 × 10 = 143.

  4. 4. Find the 22th term of the arithmetic sequence 9, 14, 19, 24, ...

    114

    First term a = 9 and common difference d = 5. Using a + (n − 1)d gives 9 + 21 × 5 = 114.

  5. 5. Find the 25th term of the arithmetic sequence 6, 18, 30, 42, ...

    294

    First term a = 6 and common difference d = 12. Using a + (n − 1)d gives 6 + 24 × 12 = 294.

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

    102

    First term a = 3 and common difference d = 9. Using a + (n − 1)d gives 3 + 11 × 9 = 102.

  7. 7. Find the 22th term of the arithmetic sequence 20, 22, 24, 26, ...

    62

    First term a = 20 and common difference d = 2. Using a + (n − 1)d gives 20 + 21 × 2 = 62.

  8. 8. Find the 15th term of the arithmetic sequence 5, 17, 29, 41, ...

    173

    First term a = 5 and common difference d = 12. Using a + (n − 1)d gives 5 + 14 × 12 = 173.

  9. 9. Find the 12th term of the arithmetic sequence 25, 36, 47, 58, ...

    146

    First term a = 25 and common difference d = 11. Using a + (n − 1)d gives 25 + 11 × 11 = 146.

  10. 10. Find the 12th term of the arithmetic sequence 15, 27, 39, 51, ...

    147

    First term a = 15 and common difference d = 12. Using a + (n − 1)d gives 15 + 11 × 12 = 147.

  11. 11. Find the 25th term of the arithmetic sequence 12, 24, 36, 48, ...

    300

    First term a = 12 and common difference d = 12. Using a + (n − 1)d gives 12 + 24 × 12 = 300.

  12. 12. 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.

12 questions · Seed 45 · 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 11th term of the arithmetic sequence 14, 19, 24, 29, ...

    11+314+319+324+3?

  2. 2. Find the 12th term of the arithmetic sequence 18, 20, 22, 24, ...

    12+618+620+622+6?

  3. 3. Find the 14th term of the arithmetic sequence 13, 23, 33, 43, ...

    14-113-123-133-1?

  4. 4. Find the 22th term of the arithmetic sequence 9, 14, 19, 24, ...

    22-139-1314-1319-13?

  5. 5. Find the 25th term of the arithmetic sequence 6, 18, 30, 42, ...

    25-196-1918-1930-19?

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

    12-93-912-921-9?

  7. 7. Find the 22th term of the arithmetic sequence 20, 22, 24, 26, ...

    22-220-222-224-2?

  8. 8. Find the 15th term of the arithmetic sequence 5, 17, 29, 41, ...

    15-105-1017-1029-10?

  9. 9. Find the 12th term of the arithmetic sequence 25, 36, 47, 58, ...

    12+1325+1336+1347+13?

  10. 10. Find the 12th term of the arithmetic sequence 15, 27, 39, 51, ...

    12+315+327+339+3?

  11. 11. Find the 25th term of the arithmetic sequence 12, 24, 36, 48, ...

    25-1312-1324-1336-13?

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

    8+1523+1527+1531+15?
12 questions · Seed 45 · 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 11th term of the arithmetic sequence 14, 19, 24, 29, ...

    64

    First term a = 14 and common difference d = 5. Using a + (n − 1)d gives 14 + 10 × 5 = 64.

  2. 2. Find the 12th term of the arithmetic sequence 18, 20, 22, 24, ...

    40

    First term a = 18 and common difference d = 2. Using a + (n − 1)d gives 18 + 11 × 2 = 40.

  3. 3. Find the 14th term of the arithmetic sequence 13, 23, 33, 43, ...

    143

    First term a = 13 and common difference d = 10. Using a + (n − 1)d gives 13 + 13 × 10 = 143.

  4. 4. Find the 22th term of the arithmetic sequence 9, 14, 19, 24, ...

    114

    First term a = 9 and common difference d = 5. Using a + (n − 1)d gives 9 + 21 × 5 = 114.

  5. 5. Find the 25th term of the arithmetic sequence 6, 18, 30, 42, ...

    294

    First term a = 6 and common difference d = 12. Using a + (n − 1)d gives 6 + 24 × 12 = 294.

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

    102

    First term a = 3 and common difference d = 9. Using a + (n − 1)d gives 3 + 11 × 9 = 102.

  7. 7. Find the 22th term of the arithmetic sequence 20, 22, 24, 26, ...

    62

    First term a = 20 and common difference d = 2. Using a + (n − 1)d gives 20 + 21 × 2 = 62.

  8. 8. Find the 15th term of the arithmetic sequence 5, 17, 29, 41, ...

    173

    First term a = 5 and common difference d = 12. Using a + (n − 1)d gives 5 + 14 × 12 = 173.

  9. 9. Find the 12th term of the arithmetic sequence 25, 36, 47, 58, ...

    146

    First term a = 25 and common difference d = 11. Using a + (n − 1)d gives 25 + 11 × 11 = 146.

  10. 10. Find the 12th term of the arithmetic sequence 15, 27, 39, 51, ...

    147

    First term a = 15 and common difference d = 12. Using a + (n − 1)d gives 15 + 11 × 12 = 147.

  11. 11. Find the 25th term of the arithmetic sequence 12, 24, 36, 48, ...

    300

    First term a = 12 and common difference d = 12. Using a + (n − 1)d gives 12 + 24 × 12 = 300.

  12. 12. 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.

12 questions · Seed 45 · Age guidance, not curriculum certification