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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 8th term of the arithmetic sequence 11, 22, 33, 44, ...

    8+311+322+333+3?

  2. 2. Find the 10th term of the arithmetic sequence 5, 17, 29, 41, ...

    10-55-517-529-5?

  3. 3. Find the 23th term of the arithmetic sequence 24, 32, 40, 48, ...

    23+124+132+140+1?

  4. 4. Find the 12th term of the arithmetic sequence 22, 32, 42, 52, ...

    12+1022+1032+1042+10?

  5. 5. Find the 20th term of the arithmetic sequence 11, 14, 17, 20, ...

    20-911-914-917-9?

  6. 6. Find the 11th term of the arithmetic sequence 20, 30, 40, 50, ...

    11+920+930+940+9?

  7. 7. Find the 12th term of the arithmetic sequence 14, 23, 32, 41, ...

    12+214+223+232+2?

  8. 8. Find the 13th term of the arithmetic sequence 18, 25, 32, 39, ...

    13+518+525+532+5?

  9. 9. Find the 18th term of the arithmetic sequence 11, 14, 17, 20, ...

    18-711-714-717-7?

  10. 10. Find the 15th term of the arithmetic sequence 3, 8, 13, 18, ...

    15-123-128-1213-12?

  11. 11. Find the 9th term of the arithmetic sequence 20, 23, 26, 29, ...

    9+1120+1123+1126+11?

  12. 12. Find the 24th term of the arithmetic sequence 7, 12, 17, 22, ...

    24-177-1712-1717-17?
12 questions · Seed 104731 · 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 8th term of the arithmetic sequence 11, 22, 33, 44, ...

    88

    First term a = 11 and common difference d = 11. Using a + (n − 1)d gives 11 + 7 × 11 = 88.

  2. 2. Find the 10th term of the arithmetic sequence 5, 17, 29, 41, ...

    113

    First term a = 5 and common difference d = 12. Using a + (n − 1)d gives 5 + 9 × 12 = 113.

  3. 3. Find the 23th term of the arithmetic sequence 24, 32, 40, 48, ...

    200

    First term a = 24 and common difference d = 8. Using a + (n − 1)d gives 24 + 22 × 8 = 200.

  4. 4. Find the 12th term of the arithmetic sequence 22, 32, 42, 52, ...

    132

    First term a = 22 and common difference d = 10. Using a + (n − 1)d gives 22 + 11 × 10 = 132.

  5. 5. Find the 20th term of the arithmetic sequence 11, 14, 17, 20, ...

    68

    First term a = 11 and common difference d = 3. Using a + (n − 1)d gives 11 + 19 × 3 = 68.

  6. 6. Find the 11th term of the arithmetic sequence 20, 30, 40, 50, ...

    120

    First term a = 20 and common difference d = 10. Using a + (n − 1)d gives 20 + 10 × 10 = 120.

  7. 7. Find the 12th term of the arithmetic sequence 14, 23, 32, 41, ...

    113

    First term a = 14 and common difference d = 9. Using a + (n − 1)d gives 14 + 11 × 9 = 113.

  8. 8. Find the 13th term of the arithmetic sequence 18, 25, 32, 39, ...

    102

    First term a = 18 and common difference d = 7. Using a + (n − 1)d gives 18 + 12 × 7 = 102.

  9. 9. Find the 18th term of the arithmetic sequence 11, 14, 17, 20, ...

    62

    First term a = 11 and common difference d = 3. Using a + (n − 1)d gives 11 + 17 × 3 = 62.

  10. 10. Find the 15th term of the arithmetic sequence 3, 8, 13, 18, ...

    73

    First term a = 3 and common difference d = 5. Using a + (n − 1)d gives 3 + 14 × 5 = 73.

  11. 11. Find the 9th term of the arithmetic sequence 20, 23, 26, 29, ...

    44

    First term a = 20 and common difference d = 3. Using a + (n − 1)d gives 20 + 8 × 3 = 44.

  12. 12. Find the 24th term of the arithmetic sequence 7, 12, 17, 22, ...

    122

    First term a = 7 and common difference d = 5. Using a + (n − 1)d gives 7 + 23 × 5 = 122.

12 questions · Seed 104731 · 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 8th term of the arithmetic sequence 11, 22, 33, 44, ...

    8+311+322+333+3?

  2. 2. Find the 10th term of the arithmetic sequence 5, 17, 29, 41, ...

    10-55-517-529-5?

  3. 3. Find the 23th term of the arithmetic sequence 24, 32, 40, 48, ...

    23+124+132+140+1?

  4. 4. Find the 12th term of the arithmetic sequence 22, 32, 42, 52, ...

    12+1022+1032+1042+10?

  5. 5. Find the 20th term of the arithmetic sequence 11, 14, 17, 20, ...

    20-911-914-917-9?

  6. 6. Find the 11th term of the arithmetic sequence 20, 30, 40, 50, ...

    11+920+930+940+9?

  7. 7. Find the 12th term of the arithmetic sequence 14, 23, 32, 41, ...

    12+214+223+232+2?

  8. 8. Find the 13th term of the arithmetic sequence 18, 25, 32, 39, ...

    13+518+525+532+5?

  9. 9. Find the 18th term of the arithmetic sequence 11, 14, 17, 20, ...

    18-711-714-717-7?

  10. 10. Find the 15th term of the arithmetic sequence 3, 8, 13, 18, ...

    15-123-128-1213-12?

  11. 11. Find the 9th term of the arithmetic sequence 20, 23, 26, 29, ...

    9+1120+1123+1126+11?

  12. 12. Find the 24th term of the arithmetic sequence 7, 12, 17, 22, ...

    24-177-1712-1717-17?
12 questions · Seed 104731 · 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 8th term of the arithmetic sequence 11, 22, 33, 44, ...

    88

    First term a = 11 and common difference d = 11. Using a + (n − 1)d gives 11 + 7 × 11 = 88.

  2. 2. Find the 10th term of the arithmetic sequence 5, 17, 29, 41, ...

    113

    First term a = 5 and common difference d = 12. Using a + (n − 1)d gives 5 + 9 × 12 = 113.

  3. 3. Find the 23th term of the arithmetic sequence 24, 32, 40, 48, ...

    200

    First term a = 24 and common difference d = 8. Using a + (n − 1)d gives 24 + 22 × 8 = 200.

  4. 4. Find the 12th term of the arithmetic sequence 22, 32, 42, 52, ...

    132

    First term a = 22 and common difference d = 10. Using a + (n − 1)d gives 22 + 11 × 10 = 132.

  5. 5. Find the 20th term of the arithmetic sequence 11, 14, 17, 20, ...

    68

    First term a = 11 and common difference d = 3. Using a + (n − 1)d gives 11 + 19 × 3 = 68.

  6. 6. Find the 11th term of the arithmetic sequence 20, 30, 40, 50, ...

    120

    First term a = 20 and common difference d = 10. Using a + (n − 1)d gives 20 + 10 × 10 = 120.

  7. 7. Find the 12th term of the arithmetic sequence 14, 23, 32, 41, ...

    113

    First term a = 14 and common difference d = 9. Using a + (n − 1)d gives 14 + 11 × 9 = 113.

  8. 8. Find the 13th term of the arithmetic sequence 18, 25, 32, 39, ...

    102

    First term a = 18 and common difference d = 7. Using a + (n − 1)d gives 18 + 12 × 7 = 102.

  9. 9. Find the 18th term of the arithmetic sequence 11, 14, 17, 20, ...

    62

    First term a = 11 and common difference d = 3. Using a + (n − 1)d gives 11 + 17 × 3 = 62.

  10. 10. Find the 15th term of the arithmetic sequence 3, 8, 13, 18, ...

    73

    First term a = 3 and common difference d = 5. Using a + (n − 1)d gives 3 + 14 × 5 = 73.

  11. 11. Find the 9th term of the arithmetic sequence 20, 23, 26, 29, ...

    44

    First term a = 20 and common difference d = 3. Using a + (n − 1)d gives 20 + 8 × 3 = 44.

  12. 12. Find the 24th term of the arithmetic sequence 7, 12, 17, 22, ...

    122

    First term a = 7 and common difference d = 5. Using a + (n − 1)d gives 7 + 23 × 5 = 122.

12 questions · Seed 104731 · Age guidance, not curriculum certification