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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 13th term of the arithmetic sequence 13, 21, 29, 37, ...

    13+013+021+029+0?

  2. 2. Find the 16th term of the arithmetic sequence 6, 10, 14, 18, ...

    16-106-1010-1014-10?

  3. 3. Find the 20th term of the arithmetic sequence 12, 24, 36, 48, ...

    20-812-824-836-8?

  4. 4. Find the 12th term of the arithmetic sequence 20, 22, 24, 26, ...

    12+820+822+824+8?

  5. 5. Find the 20th term of the arithmetic sequence 11, 19, 27, 35, ...

    20-911-919-927-9?

  6. 6. Find the 19th term of the arithmetic sequence 7, 18, 29, 40, ...

    19-127-1218-1229-12?

  7. 7. Find the 22th term of the arithmetic sequence 6, 9, 12, 15, ...

    22-166-169-1612-16?

  8. 8. Find the 8th term of the arithmetic sequence 2, 10, 18, 26, ...

    8-62-610-618-6?

  9. 9. Find the 21th term of the arithmetic sequence 13, 20, 27, 34, ...

    21-813-820-827-8?

  10. 10. Find the 16th term of the arithmetic sequence 2, 11, 20, 29, ...

    16-142-1411-1420-14?

  11. 11. Find the 12th term of the arithmetic sequence 25, 28, 31, 34, ...

    12+1325+1328+1331+13?

  12. 12. Find the 24th term of the arithmetic sequence 2, 7, 12, 17, ...

    24-222-227-2212-22?
12 questions · Seed 59 · 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 13th term of the arithmetic sequence 13, 21, 29, 37, ...

    109

    First term a = 13 and common difference d = 8. Using a + (n − 1)d gives 13 + 12 × 8 = 109.

  2. 2. Find the 16th term of the arithmetic sequence 6, 10, 14, 18, ...

    66

    First term a = 6 and common difference d = 4. Using a + (n − 1)d gives 6 + 15 × 4 = 66.

  3. 3. Find the 20th term of the arithmetic sequence 12, 24, 36, 48, ...

    240

    First term a = 12 and common difference d = 12. Using a + (n − 1)d gives 12 + 19 × 12 = 240.

  4. 4. Find the 12th term of the arithmetic sequence 20, 22, 24, 26, ...

    42

    First term a = 20 and common difference d = 2. Using a + (n − 1)d gives 20 + 11 × 2 = 42.

  5. 5. Find the 20th term of the arithmetic sequence 11, 19, 27, 35, ...

    163

    First term a = 11 and common difference d = 8. Using a + (n − 1)d gives 11 + 19 × 8 = 163.

  6. 6. Find the 19th term of the arithmetic sequence 7, 18, 29, 40, ...

    205

    First term a = 7 and common difference d = 11. Using a + (n − 1)d gives 7 + 18 × 11 = 205.

  7. 7. Find the 22th term of the arithmetic sequence 6, 9, 12, 15, ...

    69

    First term a = 6 and common difference d = 3. Using a + (n − 1)d gives 6 + 21 × 3 = 69.

  8. 8. Find the 8th term of the arithmetic sequence 2, 10, 18, 26, ...

    58

    First term a = 2 and common difference d = 8. Using a + (n − 1)d gives 2 + 7 × 8 = 58.

  9. 9. Find the 21th term of the arithmetic sequence 13, 20, 27, 34, ...

    153

    First term a = 13 and common difference d = 7. Using a + (n − 1)d gives 13 + 20 × 7 = 153.

  10. 10. Find the 16th term of the arithmetic sequence 2, 11, 20, 29, ...

    137

    First term a = 2 and common difference d = 9. Using a + (n − 1)d gives 2 + 15 × 9 = 137.

  11. 11. Find the 12th term of the arithmetic sequence 25, 28, 31, 34, ...

    58

    First term a = 25 and common difference d = 3. Using a + (n − 1)d gives 25 + 11 × 3 = 58.

  12. 12. Find the 24th term of the arithmetic sequence 2, 7, 12, 17, ...

    117

    First term a = 2 and common difference d = 5. Using a + (n − 1)d gives 2 + 23 × 5 = 117.

12 questions · Seed 59 · 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 13th term of the arithmetic sequence 13, 21, 29, 37, ...

    13+013+021+029+0?

  2. 2. Find the 16th term of the arithmetic sequence 6, 10, 14, 18, ...

    16-106-1010-1014-10?

  3. 3. Find the 20th term of the arithmetic sequence 12, 24, 36, 48, ...

    20-812-824-836-8?

  4. 4. Find the 12th term of the arithmetic sequence 20, 22, 24, 26, ...

    12+820+822+824+8?

  5. 5. Find the 20th term of the arithmetic sequence 11, 19, 27, 35, ...

    20-911-919-927-9?

  6. 6. Find the 19th term of the arithmetic sequence 7, 18, 29, 40, ...

    19-127-1218-1229-12?

  7. 7. Find the 22th term of the arithmetic sequence 6, 9, 12, 15, ...

    22-166-169-1612-16?

  8. 8. Find the 8th term of the arithmetic sequence 2, 10, 18, 26, ...

    8-62-610-618-6?

  9. 9. Find the 21th term of the arithmetic sequence 13, 20, 27, 34, ...

    21-813-820-827-8?

  10. 10. Find the 16th term of the arithmetic sequence 2, 11, 20, 29, ...

    16-142-1411-1420-14?

  11. 11. Find the 12th term of the arithmetic sequence 25, 28, 31, 34, ...

    12+1325+1328+1331+13?

  12. 12. Find the 24th term of the arithmetic sequence 2, 7, 12, 17, ...

    24-222-227-2212-22?
12 questions · Seed 59 · 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 13th term of the arithmetic sequence 13, 21, 29, 37, ...

    109

    First term a = 13 and common difference d = 8. Using a + (n − 1)d gives 13 + 12 × 8 = 109.

  2. 2. Find the 16th term of the arithmetic sequence 6, 10, 14, 18, ...

    66

    First term a = 6 and common difference d = 4. Using a + (n − 1)d gives 6 + 15 × 4 = 66.

  3. 3. Find the 20th term of the arithmetic sequence 12, 24, 36, 48, ...

    240

    First term a = 12 and common difference d = 12. Using a + (n − 1)d gives 12 + 19 × 12 = 240.

  4. 4. Find the 12th term of the arithmetic sequence 20, 22, 24, 26, ...

    42

    First term a = 20 and common difference d = 2. Using a + (n − 1)d gives 20 + 11 × 2 = 42.

  5. 5. Find the 20th term of the arithmetic sequence 11, 19, 27, 35, ...

    163

    First term a = 11 and common difference d = 8. Using a + (n − 1)d gives 11 + 19 × 8 = 163.

  6. 6. Find the 19th term of the arithmetic sequence 7, 18, 29, 40, ...

    205

    First term a = 7 and common difference d = 11. Using a + (n − 1)d gives 7 + 18 × 11 = 205.

  7. 7. Find the 22th term of the arithmetic sequence 6, 9, 12, 15, ...

    69

    First term a = 6 and common difference d = 3. Using a + (n − 1)d gives 6 + 21 × 3 = 69.

  8. 8. Find the 8th term of the arithmetic sequence 2, 10, 18, 26, ...

    58

    First term a = 2 and common difference d = 8. Using a + (n − 1)d gives 2 + 7 × 8 = 58.

  9. 9. Find the 21th term of the arithmetic sequence 13, 20, 27, 34, ...

    153

    First term a = 13 and common difference d = 7. Using a + (n − 1)d gives 13 + 20 × 7 = 153.

  10. 10. Find the 16th term of the arithmetic sequence 2, 11, 20, 29, ...

    137

    First term a = 2 and common difference d = 9. Using a + (n − 1)d gives 2 + 15 × 9 = 137.

  11. 11. Find the 12th term of the arithmetic sequence 25, 28, 31, 34, ...

    58

    First term a = 25 and common difference d = 3. Using a + (n − 1)d gives 25 + 11 × 3 = 58.

  12. 12. Find the 24th term of the arithmetic sequence 2, 7, 12, 17, ...

    117

    First term a = 2 and common difference d = 5. Using a + (n − 1)d gives 2 + 23 × 5 = 117.

12 questions · Seed 59 · Age guidance, not curriculum certification