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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 15th term of the arithmetic sequence 22, 28, 34, 40, ...

    15+722+728+734+7?

  2. 2. Find the 13th term of the arithmetic sequence 5, 7, 9, 11, ...

    13-85-87-89-8?

  3. 3. Find the 10th term of the arithmetic sequence 25, 36, 47, 58, ...

    10+1525+1536+1547+15?

  4. 4. Find the 25th term of the arithmetic sequence 15, 19, 23, 27, ...

    25-1015-1019-1023-10?

  5. 5. Find the 23th term of the arithmetic sequence 24, 36, 48, 60, ...

    23+124+136+148+1?

  6. 6. Find the 24th term of the arithmetic sequence 25, 32, 39, 46, ...

    24+125+132+139+1?

  7. 7. Find the 10th term of the arithmetic sequence 12, 18, 24, 30, ...

    10+212+218+224+2?

  8. 8. Find the 18th term of the arithmetic sequence 2, 12, 22, 32, ...

    18-162-1612-1622-16?

  9. 9. Find the 20th term of the arithmetic sequence 6, 15, 24, 33, ...

    20-146-1415-1424-14?

  10. 10. Find the 20th term of the arithmetic sequence 11, 16, 21, 26, ...

    20-911-916-921-9?

  11. 11. Find the 14th term of the arithmetic sequence 22, 24, 26, 28, ...

    14+822+824+826+8?

  12. 12. Find the 17th term of the arithmetic sequence 23, 26, 29, 32, ...

    17+623+626+629+6?
12 questions · Seed 50 · 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 15th term of the arithmetic sequence 22, 28, 34, 40, ...

    106

    First term a = 22 and common difference d = 6. Using a + (n − 1)d gives 22 + 14 × 6 = 106.

  2. 2. Find the 13th term of the arithmetic sequence 5, 7, 9, 11, ...

    29

    First term a = 5 and common difference d = 2. Using a + (n − 1)d gives 5 + 12 × 2 = 29.

  3. 3. Find the 10th term of the arithmetic sequence 25, 36, 47, 58, ...

    124

    First term a = 25 and common difference d = 11. Using a + (n − 1)d gives 25 + 9 × 11 = 124.

  4. 4. Find the 25th term of the arithmetic sequence 15, 19, 23, 27, ...

    111

    First term a = 15 and common difference d = 4. Using a + (n − 1)d gives 15 + 24 × 4 = 111.

  5. 5. Find the 23th term of the arithmetic sequence 24, 36, 48, 60, ...

    288

    First term a = 24 and common difference d = 12. Using a + (n − 1)d gives 24 + 22 × 12 = 288.

  6. 6. Find the 24th term of the arithmetic sequence 25, 32, 39, 46, ...

    186

    First term a = 25 and common difference d = 7. Using a + (n − 1)d gives 25 + 23 × 7 = 186.

  7. 7. Find the 10th term of the arithmetic sequence 12, 18, 24, 30, ...

    66

    First term a = 12 and common difference d = 6. Using a + (n − 1)d gives 12 + 9 × 6 = 66.

  8. 8. Find the 18th term of the arithmetic sequence 2, 12, 22, 32, ...

    172

    First term a = 2 and common difference d = 10. Using a + (n − 1)d gives 2 + 17 × 10 = 172.

  9. 9. Find the 20th term of the arithmetic sequence 6, 15, 24, 33, ...

    177

    First term a = 6 and common difference d = 9. Using a + (n − 1)d gives 6 + 19 × 9 = 177.

  10. 10. Find the 20th term of the arithmetic sequence 11, 16, 21, 26, ...

    106

    First term a = 11 and common difference d = 5. Using a + (n − 1)d gives 11 + 19 × 5 = 106.

  11. 11. Find the 14th term of the arithmetic sequence 22, 24, 26, 28, ...

    48

    First term a = 22 and common difference d = 2. Using a + (n − 1)d gives 22 + 13 × 2 = 48.

  12. 12. Find the 17th term of the arithmetic sequence 23, 26, 29, 32, ...

    71

    First term a = 23 and common difference d = 3. Using a + (n − 1)d gives 23 + 16 × 3 = 71.

12 questions · Seed 50 · 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 15th term of the arithmetic sequence 22, 28, 34, 40, ...

    15+722+728+734+7?

  2. 2. Find the 13th term of the arithmetic sequence 5, 7, 9, 11, ...

    13-85-87-89-8?

  3. 3. Find the 10th term of the arithmetic sequence 25, 36, 47, 58, ...

    10+1525+1536+1547+15?

  4. 4. Find the 25th term of the arithmetic sequence 15, 19, 23, 27, ...

    25-1015-1019-1023-10?

  5. 5. Find the 23th term of the arithmetic sequence 24, 36, 48, 60, ...

    23+124+136+148+1?

  6. 6. Find the 24th term of the arithmetic sequence 25, 32, 39, 46, ...

    24+125+132+139+1?

  7. 7. Find the 10th term of the arithmetic sequence 12, 18, 24, 30, ...

    10+212+218+224+2?

  8. 8. Find the 18th term of the arithmetic sequence 2, 12, 22, 32, ...

    18-162-1612-1622-16?

  9. 9. Find the 20th term of the arithmetic sequence 6, 15, 24, 33, ...

    20-146-1415-1424-14?

  10. 10. Find the 20th term of the arithmetic sequence 11, 16, 21, 26, ...

    20-911-916-921-9?

  11. 11. Find the 14th term of the arithmetic sequence 22, 24, 26, 28, ...

    14+822+824+826+8?

  12. 12. Find the 17th term of the arithmetic sequence 23, 26, 29, 32, ...

    17+623+626+629+6?
12 questions · Seed 50 · 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 15th term of the arithmetic sequence 22, 28, 34, 40, ...

    106

    First term a = 22 and common difference d = 6. Using a + (n − 1)d gives 22 + 14 × 6 = 106.

  2. 2. Find the 13th term of the arithmetic sequence 5, 7, 9, 11, ...

    29

    First term a = 5 and common difference d = 2. Using a + (n − 1)d gives 5 + 12 × 2 = 29.

  3. 3. Find the 10th term of the arithmetic sequence 25, 36, 47, 58, ...

    124

    First term a = 25 and common difference d = 11. Using a + (n − 1)d gives 25 + 9 × 11 = 124.

  4. 4. Find the 25th term of the arithmetic sequence 15, 19, 23, 27, ...

    111

    First term a = 15 and common difference d = 4. Using a + (n − 1)d gives 15 + 24 × 4 = 111.

  5. 5. Find the 23th term of the arithmetic sequence 24, 36, 48, 60, ...

    288

    First term a = 24 and common difference d = 12. Using a + (n − 1)d gives 24 + 22 × 12 = 288.

  6. 6. Find the 24th term of the arithmetic sequence 25, 32, 39, 46, ...

    186

    First term a = 25 and common difference d = 7. Using a + (n − 1)d gives 25 + 23 × 7 = 186.

  7. 7. Find the 10th term of the arithmetic sequence 12, 18, 24, 30, ...

    66

    First term a = 12 and common difference d = 6. Using a + (n − 1)d gives 12 + 9 × 6 = 66.

  8. 8. Find the 18th term of the arithmetic sequence 2, 12, 22, 32, ...

    172

    First term a = 2 and common difference d = 10. Using a + (n − 1)d gives 2 + 17 × 10 = 172.

  9. 9. Find the 20th term of the arithmetic sequence 6, 15, 24, 33, ...

    177

    First term a = 6 and common difference d = 9. Using a + (n − 1)d gives 6 + 19 × 9 = 177.

  10. 10. Find the 20th term of the arithmetic sequence 11, 16, 21, 26, ...

    106

    First term a = 11 and common difference d = 5. Using a + (n − 1)d gives 11 + 19 × 5 = 106.

  11. 11. Find the 14th term of the arithmetic sequence 22, 24, 26, 28, ...

    48

    First term a = 22 and common difference d = 2. Using a + (n − 1)d gives 22 + 13 × 2 = 48.

  12. 12. Find the 17th term of the arithmetic sequence 23, 26, 29, 32, ...

    71

    First term a = 23 and common difference d = 3. Using a + (n − 1)d gives 23 + 16 × 3 = 71.

12 questions · Seed 50 · Age guidance, not curriculum certification