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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 9th term of the arithmetic sequence 5, 12, 19, 26, ...

    9-45-412-419-4?

  2. 2. Find the 16th term of the arithmetic sequence 19, 23, 27, 31, ...

    16+319+323+327+3?

  3. 3. Find the 24th term of the arithmetic sequence 24, 35, 46, 57, ...

    24+024+035+046+0?

  4. 4. Find the 9th term of the arithmetic sequence 14, 17, 20, 23, ...

    9+514+517+520+5?

  5. 5. Find the 22th term of the arithmetic sequence 17, 25, 33, 41, ...

    22-517-525-533-5?

  6. 6. Find the 24th term of the arithmetic sequence 8, 11, 14, 17, ...

    24-168-1611-1614-16?

  7. 7. Find the 16th term of the arithmetic sequence 14, 24, 34, 44, ...

    16-214-224-234-2?

  8. 8. Find the 23th term of the arithmetic sequence 6, 16, 26, 36, ...

    23-176-1716-1726-17?

  9. 9. Find the 13th term of the arithmetic sequence 8, 17, 26, 35, ...

    13-58-517-526-5?

  10. 10. Find the 8th term of the arithmetic sequence 6, 10, 14, 18, ...

    8-26-210-214-2?

  11. 11. Find the 23th term of the arithmetic sequence 15, 27, 39, 51, ...

    23-815-827-839-8?

  12. 12. Find the 15th term of the arithmetic sequence 2, 8, 14, 20, ...

    15-132-138-1314-13?
12 questions · Seed 54 · 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 9th term of the arithmetic sequence 5, 12, 19, 26, ...

    61

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

  2. 2. Find the 16th term of the arithmetic sequence 19, 23, 27, 31, ...

    79

    First term a = 19 and common difference d = 4. Using a + (n − 1)d gives 19 + 15 × 4 = 79.

  3. 3. Find the 24th term of the arithmetic sequence 24, 35, 46, 57, ...

    277

    First term a = 24 and common difference d = 11. Using a + (n − 1)d gives 24 + 23 × 11 = 277.

  4. 4. Find the 9th term of the arithmetic sequence 14, 17, 20, 23, ...

    38

    First term a = 14 and common difference d = 3. Using a + (n − 1)d gives 14 + 8 × 3 = 38.

  5. 5. Find the 22th term of the arithmetic sequence 17, 25, 33, 41, ...

    185

    First term a = 17 and common difference d = 8. Using a + (n − 1)d gives 17 + 21 × 8 = 185.

  6. 6. Find the 24th term of the arithmetic sequence 8, 11, 14, 17, ...

    77

    First term a = 8 and common difference d = 3. Using a + (n − 1)d gives 8 + 23 × 3 = 77.

  7. 7. Find the 16th term of the arithmetic sequence 14, 24, 34, 44, ...

    164

    First term a = 14 and common difference d = 10. Using a + (n − 1)d gives 14 + 15 × 10 = 164.

  8. 8. Find the 23th term of the arithmetic sequence 6, 16, 26, 36, ...

    226

    First term a = 6 and common difference d = 10. Using a + (n − 1)d gives 6 + 22 × 10 = 226.

  9. 9. Find the 13th term of the arithmetic sequence 8, 17, 26, 35, ...

    116

    First term a = 8 and common difference d = 9. Using a + (n − 1)d gives 8 + 12 × 9 = 116.

  10. 10. Find the 8th term of the arithmetic sequence 6, 10, 14, 18, ...

    34

    First term a = 6 and common difference d = 4. Using a + (n − 1)d gives 6 + 7 × 4 = 34.

  11. 11. Find the 23th term of the arithmetic sequence 15, 27, 39, 51, ...

    279

    First term a = 15 and common difference d = 12. Using a + (n − 1)d gives 15 + 22 × 12 = 279.

  12. 12. Find the 15th term of the arithmetic sequence 2, 8, 14, 20, ...

    86

    First term a = 2 and common difference d = 6. Using a + (n − 1)d gives 2 + 14 × 6 = 86.

12 questions · Seed 54 · 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 9th term of the arithmetic sequence 5, 12, 19, 26, ...

    9-45-412-419-4?

  2. 2. Find the 16th term of the arithmetic sequence 19, 23, 27, 31, ...

    16+319+323+327+3?

  3. 3. Find the 24th term of the arithmetic sequence 24, 35, 46, 57, ...

    24+024+035+046+0?

  4. 4. Find the 9th term of the arithmetic sequence 14, 17, 20, 23, ...

    9+514+517+520+5?

  5. 5. Find the 22th term of the arithmetic sequence 17, 25, 33, 41, ...

    22-517-525-533-5?

  6. 6. Find the 24th term of the arithmetic sequence 8, 11, 14, 17, ...

    24-168-1611-1614-16?

  7. 7. Find the 16th term of the arithmetic sequence 14, 24, 34, 44, ...

    16-214-224-234-2?

  8. 8. Find the 23th term of the arithmetic sequence 6, 16, 26, 36, ...

    23-176-1716-1726-17?

  9. 9. Find the 13th term of the arithmetic sequence 8, 17, 26, 35, ...

    13-58-517-526-5?

  10. 10. Find the 8th term of the arithmetic sequence 6, 10, 14, 18, ...

    8-26-210-214-2?

  11. 11. Find the 23th term of the arithmetic sequence 15, 27, 39, 51, ...

    23-815-827-839-8?

  12. 12. Find the 15th term of the arithmetic sequence 2, 8, 14, 20, ...

    15-132-138-1314-13?
12 questions · Seed 54 · 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 9th term of the arithmetic sequence 5, 12, 19, 26, ...

    61

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

  2. 2. Find the 16th term of the arithmetic sequence 19, 23, 27, 31, ...

    79

    First term a = 19 and common difference d = 4. Using a + (n − 1)d gives 19 + 15 × 4 = 79.

  3. 3. Find the 24th term of the arithmetic sequence 24, 35, 46, 57, ...

    277

    First term a = 24 and common difference d = 11. Using a + (n − 1)d gives 24 + 23 × 11 = 277.

  4. 4. Find the 9th term of the arithmetic sequence 14, 17, 20, 23, ...

    38

    First term a = 14 and common difference d = 3. Using a + (n − 1)d gives 14 + 8 × 3 = 38.

  5. 5. Find the 22th term of the arithmetic sequence 17, 25, 33, 41, ...

    185

    First term a = 17 and common difference d = 8. Using a + (n − 1)d gives 17 + 21 × 8 = 185.

  6. 6. Find the 24th term of the arithmetic sequence 8, 11, 14, 17, ...

    77

    First term a = 8 and common difference d = 3. Using a + (n − 1)d gives 8 + 23 × 3 = 77.

  7. 7. Find the 16th term of the arithmetic sequence 14, 24, 34, 44, ...

    164

    First term a = 14 and common difference d = 10. Using a + (n − 1)d gives 14 + 15 × 10 = 164.

  8. 8. Find the 23th term of the arithmetic sequence 6, 16, 26, 36, ...

    226

    First term a = 6 and common difference d = 10. Using a + (n − 1)d gives 6 + 22 × 10 = 226.

  9. 9. Find the 13th term of the arithmetic sequence 8, 17, 26, 35, ...

    116

    First term a = 8 and common difference d = 9. Using a + (n − 1)d gives 8 + 12 × 9 = 116.

  10. 10. Find the 8th term of the arithmetic sequence 6, 10, 14, 18, ...

    34

    First term a = 6 and common difference d = 4. Using a + (n − 1)d gives 6 + 7 × 4 = 34.

  11. 11. Find the 23th term of the arithmetic sequence 15, 27, 39, 51, ...

    279

    First term a = 15 and common difference d = 12. Using a + (n − 1)d gives 15 + 22 × 12 = 279.

  12. 12. Find the 15th term of the arithmetic sequence 2, 8, 14, 20, ...

    86

    First term a = 2 and common difference d = 6. Using a + (n − 1)d gives 2 + 14 × 6 = 86.

12 questions · Seed 54 · Age guidance, not curriculum certification