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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 8th term of the arithmetic sequence 5, 13, 21, 29, ...

    8-35-313-321-3?

  2. 2. Find the 15th term of the arithmetic sequence 3, 14, 25, 36, ...

    15-123-1214-1225-12?

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

    10-82-89-816-8?

  4. 4. Find the 20th term of the arithmetic sequence 3, 10, 17, 24, ...

    20-173-1710-1717-17?

  5. 5. Find the 11th term of the arithmetic sequence 17, 25, 33, 41, ...

    11+617+625+633+6?

  6. 6. Find the 8th term of the arithmetic sequence 17, 26, 35, 44, ...

    8+917+926+935+9?

  7. 7. Find the 22th term of the arithmetic sequence 16, 27, 38, 49, ...

    22-616-627-638-6?

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

    23-149-1416-1423-14?

  9. 9. Find the 21th term of the arithmetic sequence 24, 29, 34, 39, ...

    21+324+329+334+3?

  10. 10. Find the 22th term of the arithmetic sequence 6, 15, 24, 33, ...

    22-166-1615-1624-16?

  11. 11. Find the 21th term of the arithmetic sequence 19, 31, 43, 55, ...

    21-219-231-243-2?

  12. 12. Find the 21th term of the arithmetic sequence 9, 16, 23, 30, ...

    21-129-1216-1223-12?
12 questions · Seed 57 · 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 8th term of the arithmetic sequence 5, 13, 21, 29, ...

    61

    First term a = 5 and common difference d = 8. Using a + (n − 1)d gives 5 + 7 × 8 = 61.

  2. 2. Find the 15th term of the arithmetic sequence 3, 14, 25, 36, ...

    157

    First term a = 3 and common difference d = 11. Using a + (n − 1)d gives 3 + 14 × 11 = 157.

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

    65

    First term a = 2 and common difference d = 7. Using a + (n − 1)d gives 2 + 9 × 7 = 65.

  4. 4. Find the 20th term of the arithmetic sequence 3, 10, 17, 24, ...

    136

    First term a = 3 and common difference d = 7. Using a + (n − 1)d gives 3 + 19 × 7 = 136.

  5. 5. Find the 11th term of the arithmetic sequence 17, 25, 33, 41, ...

    97

    First term a = 17 and common difference d = 8. Using a + (n − 1)d gives 17 + 10 × 8 = 97.

  6. 6. Find the 8th term of the arithmetic sequence 17, 26, 35, 44, ...

    80

    First term a = 17 and common difference d = 9. Using a + (n − 1)d gives 17 + 7 × 9 = 80.

  7. 7. Find the 22th term of the arithmetic sequence 16, 27, 38, 49, ...

    247

    First term a = 16 and common difference d = 11. Using a + (n − 1)d gives 16 + 21 × 11 = 247.

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

    163

    First term a = 9 and common difference d = 7. Using a + (n − 1)d gives 9 + 22 × 7 = 163.

  9. 9. Find the 21th term of the arithmetic sequence 24, 29, 34, 39, ...

    124

    First term a = 24 and common difference d = 5. Using a + (n − 1)d gives 24 + 20 × 5 = 124.

  10. 10. Find the 22th term of the arithmetic sequence 6, 15, 24, 33, ...

    195

    First term a = 6 and common difference d = 9. Using a + (n − 1)d gives 6 + 21 × 9 = 195.

  11. 11. Find the 21th term of the arithmetic sequence 19, 31, 43, 55, ...

    259

    First term a = 19 and common difference d = 12. Using a + (n − 1)d gives 19 + 20 × 12 = 259.

  12. 12. Find the 21th term of the arithmetic sequence 9, 16, 23, 30, ...

    149

    First term a = 9 and common difference d = 7. Using a + (n − 1)d gives 9 + 20 × 7 = 149.

12 questions · Seed 57 · 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 8th term of the arithmetic sequence 5, 13, 21, 29, ...

    8-35-313-321-3?

  2. 2. Find the 15th term of the arithmetic sequence 3, 14, 25, 36, ...

    15-123-1214-1225-12?

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

    10-82-89-816-8?

  4. 4. Find the 20th term of the arithmetic sequence 3, 10, 17, 24, ...

    20-173-1710-1717-17?

  5. 5. Find the 11th term of the arithmetic sequence 17, 25, 33, 41, ...

    11+617+625+633+6?

  6. 6. Find the 8th term of the arithmetic sequence 17, 26, 35, 44, ...

    8+917+926+935+9?

  7. 7. Find the 22th term of the arithmetic sequence 16, 27, 38, 49, ...

    22-616-627-638-6?

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

    23-149-1416-1423-14?

  9. 9. Find the 21th term of the arithmetic sequence 24, 29, 34, 39, ...

    21+324+329+334+3?

  10. 10. Find the 22th term of the arithmetic sequence 6, 15, 24, 33, ...

    22-166-1615-1624-16?

  11. 11. Find the 21th term of the arithmetic sequence 19, 31, 43, 55, ...

    21-219-231-243-2?

  12. 12. Find the 21th term of the arithmetic sequence 9, 16, 23, 30, ...

    21-129-1216-1223-12?
12 questions · Seed 57 · 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 8th term of the arithmetic sequence 5, 13, 21, 29, ...

    61

    First term a = 5 and common difference d = 8. Using a + (n − 1)d gives 5 + 7 × 8 = 61.

  2. 2. Find the 15th term of the arithmetic sequence 3, 14, 25, 36, ...

    157

    First term a = 3 and common difference d = 11. Using a + (n − 1)d gives 3 + 14 × 11 = 157.

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

    65

    First term a = 2 and common difference d = 7. Using a + (n − 1)d gives 2 + 9 × 7 = 65.

  4. 4. Find the 20th term of the arithmetic sequence 3, 10, 17, 24, ...

    136

    First term a = 3 and common difference d = 7. Using a + (n − 1)d gives 3 + 19 × 7 = 136.

  5. 5. Find the 11th term of the arithmetic sequence 17, 25, 33, 41, ...

    97

    First term a = 17 and common difference d = 8. Using a + (n − 1)d gives 17 + 10 × 8 = 97.

  6. 6. Find the 8th term of the arithmetic sequence 17, 26, 35, 44, ...

    80

    First term a = 17 and common difference d = 9. Using a + (n − 1)d gives 17 + 7 × 9 = 80.

  7. 7. Find the 22th term of the arithmetic sequence 16, 27, 38, 49, ...

    247

    First term a = 16 and common difference d = 11. Using a + (n − 1)d gives 16 + 21 × 11 = 247.

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

    163

    First term a = 9 and common difference d = 7. Using a + (n − 1)d gives 9 + 22 × 7 = 163.

  9. 9. Find the 21th term of the arithmetic sequence 24, 29, 34, 39, ...

    124

    First term a = 24 and common difference d = 5. Using a + (n − 1)d gives 24 + 20 × 5 = 124.

  10. 10. Find the 22th term of the arithmetic sequence 6, 15, 24, 33, ...

    195

    First term a = 6 and common difference d = 9. Using a + (n − 1)d gives 6 + 21 × 9 = 195.

  11. 11. Find the 21th term of the arithmetic sequence 19, 31, 43, 55, ...

    259

    First term a = 19 and common difference d = 12. Using a + (n − 1)d gives 19 + 20 × 12 = 259.

  12. 12. Find the 21th term of the arithmetic sequence 9, 16, 23, 30, ...

    149

    First term a = 9 and common difference d = 7. Using a + (n − 1)d gives 9 + 20 × 7 = 149.

12 questions · Seed 57 · Age guidance, not curriculum certification