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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 15th term of the arithmetic sequence 9, 11, 13, 15, ...

    15-69-611-613-6?

  2. 2. Find the 8th term of the arithmetic sequence 20, 29, 38, 47, ...

    8+1220+1229+1238+12?

  3. 3. Find the 10th term of the arithmetic sequence 6, 12, 18, 24, ...

    10-46-412-418-4?

  4. 4. Find the 9th term of the arithmetic sequence 9, 20, 31, 42, ...

    9+09+020+031+0?

  5. 5. Find the 12th term of the arithmetic sequence 19, 22, 25, 28, ...

    12+719+722+725+7?

  6. 6. Find the 8th term of the arithmetic sequence 6, 8, 10, 12, ...

    8-26-28-210-2?

  7. 7. Find the 8th term of the arithmetic sequence 5, 14, 23, 32, ...

    8-35-314-323-3?

  8. 8. Find the 13th term of the arithmetic sequence 12, 24, 36, 48, ...

    13-112-124-136-1?

  9. 9. Find the 9th term of the arithmetic sequence 18, 28, 38, 48, ...

    9+918+928+938+9?

  10. 10. Find the 23th term of the arithmetic sequence 14, 19, 24, 29, ...

    23-914-919-924-9?

  11. 11. Find the 15th term of the arithmetic sequence 14, 25, 36, 47, ...

    15-114-125-136-1?

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

    13-103-1013-1023-10?
12 questions · Seed 56 · 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 15th term of the arithmetic sequence 9, 11, 13, 15, ...

    37

    First term a = 9 and common difference d = 2. Using a + (n − 1)d gives 9 + 14 × 2 = 37.

  2. 2. Find the 8th term of the arithmetic sequence 20, 29, 38, 47, ...

    83

    First term a = 20 and common difference d = 9. Using a + (n − 1)d gives 20 + 7 × 9 = 83.

  3. 3. Find the 10th term of the arithmetic sequence 6, 12, 18, 24, ...

    60

    First term a = 6 and common difference d = 6. Using a + (n − 1)d gives 6 + 9 × 6 = 60.

  4. 4. Find the 9th term of the arithmetic sequence 9, 20, 31, 42, ...

    97

    First term a = 9 and common difference d = 11. Using a + (n − 1)d gives 9 + 8 × 11 = 97.

  5. 5. Find the 12th term of the arithmetic sequence 19, 22, 25, 28, ...

    52

    First term a = 19 and common difference d = 3. Using a + (n − 1)d gives 19 + 11 × 3 = 52.

  6. 6. Find the 8th term of the arithmetic sequence 6, 8, 10, 12, ...

    20

    First term a = 6 and common difference d = 2. Using a + (n − 1)d gives 6 + 7 × 2 = 20.

  7. 7. Find the 8th term of the arithmetic sequence 5, 14, 23, 32, ...

    68

    First term a = 5 and common difference d = 9. Using a + (n − 1)d gives 5 + 7 × 9 = 68.

  8. 8. Find the 13th term of the arithmetic sequence 12, 24, 36, 48, ...

    156

    First term a = 12 and common difference d = 12. Using a + (n − 1)d gives 12 + 12 × 12 = 156.

  9. 9. Find the 9th term of the arithmetic sequence 18, 28, 38, 48, ...

    98

    First term a = 18 and common difference d = 10. Using a + (n − 1)d gives 18 + 8 × 10 = 98.

  10. 10. Find the 23th term of the arithmetic sequence 14, 19, 24, 29, ...

    124

    First term a = 14 and common difference d = 5. Using a + (n − 1)d gives 14 + 22 × 5 = 124.

  11. 11. Find the 15th term of the arithmetic sequence 14, 25, 36, 47, ...

    168

    First term a = 14 and common difference d = 11. Using a + (n − 1)d gives 14 + 14 × 11 = 168.

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

    123

    First term a = 3 and common difference d = 10. Using a + (n − 1)d gives 3 + 12 × 10 = 123.

12 questions · Seed 56 · 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 15th term of the arithmetic sequence 9, 11, 13, 15, ...

    15-69-611-613-6?

  2. 2. Find the 8th term of the arithmetic sequence 20, 29, 38, 47, ...

    8+1220+1229+1238+12?

  3. 3. Find the 10th term of the arithmetic sequence 6, 12, 18, 24, ...

    10-46-412-418-4?

  4. 4. Find the 9th term of the arithmetic sequence 9, 20, 31, 42, ...

    9+09+020+031+0?

  5. 5. Find the 12th term of the arithmetic sequence 19, 22, 25, 28, ...

    12+719+722+725+7?

  6. 6. Find the 8th term of the arithmetic sequence 6, 8, 10, 12, ...

    8-26-28-210-2?

  7. 7. Find the 8th term of the arithmetic sequence 5, 14, 23, 32, ...

    8-35-314-323-3?

  8. 8. Find the 13th term of the arithmetic sequence 12, 24, 36, 48, ...

    13-112-124-136-1?

  9. 9. Find the 9th term of the arithmetic sequence 18, 28, 38, 48, ...

    9+918+928+938+9?

  10. 10. Find the 23th term of the arithmetic sequence 14, 19, 24, 29, ...

    23-914-919-924-9?

  11. 11. Find the 15th term of the arithmetic sequence 14, 25, 36, 47, ...

    15-114-125-136-1?

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

    13-103-1013-1023-10?
12 questions · Seed 56 · 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 15th term of the arithmetic sequence 9, 11, 13, 15, ...

    37

    First term a = 9 and common difference d = 2. Using a + (n − 1)d gives 9 + 14 × 2 = 37.

  2. 2. Find the 8th term of the arithmetic sequence 20, 29, 38, 47, ...

    83

    First term a = 20 and common difference d = 9. Using a + (n − 1)d gives 20 + 7 × 9 = 83.

  3. 3. Find the 10th term of the arithmetic sequence 6, 12, 18, 24, ...

    60

    First term a = 6 and common difference d = 6. Using a + (n − 1)d gives 6 + 9 × 6 = 60.

  4. 4. Find the 9th term of the arithmetic sequence 9, 20, 31, 42, ...

    97

    First term a = 9 and common difference d = 11. Using a + (n − 1)d gives 9 + 8 × 11 = 97.

  5. 5. Find the 12th term of the arithmetic sequence 19, 22, 25, 28, ...

    52

    First term a = 19 and common difference d = 3. Using a + (n − 1)d gives 19 + 11 × 3 = 52.

  6. 6. Find the 8th term of the arithmetic sequence 6, 8, 10, 12, ...

    20

    First term a = 6 and common difference d = 2. Using a + (n − 1)d gives 6 + 7 × 2 = 20.

  7. 7. Find the 8th term of the arithmetic sequence 5, 14, 23, 32, ...

    68

    First term a = 5 and common difference d = 9. Using a + (n − 1)d gives 5 + 7 × 9 = 68.

  8. 8. Find the 13th term of the arithmetic sequence 12, 24, 36, 48, ...

    156

    First term a = 12 and common difference d = 12. Using a + (n − 1)d gives 12 + 12 × 12 = 156.

  9. 9. Find the 9th term of the arithmetic sequence 18, 28, 38, 48, ...

    98

    First term a = 18 and common difference d = 10. Using a + (n − 1)d gives 18 + 8 × 10 = 98.

  10. 10. Find the 23th term of the arithmetic sequence 14, 19, 24, 29, ...

    124

    First term a = 14 and common difference d = 5. Using a + (n − 1)d gives 14 + 22 × 5 = 124.

  11. 11. Find the 15th term of the arithmetic sequence 14, 25, 36, 47, ...

    168

    First term a = 14 and common difference d = 11. Using a + (n − 1)d gives 14 + 14 × 11 = 168.

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

    123

    First term a = 3 and common difference d = 10. Using a + (n − 1)d gives 3 + 12 × 10 = 123.

12 questions · Seed 56 · Age guidance, not curriculum certification