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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 16th term of the arithmetic sequence 11, 21, 31, 41, ...

    16-511-521-531-5?

  2. 2. Find the 12th term of the arithmetic sequence 20, 31, 42, 53, ...

    12+820+831+842+8?

  3. 3. Find the 17th term of the arithmetic sequence 25, 33, 41, 49, ...

    17+825+833+841+8?

  4. 4. Find the 9th term of the arithmetic sequence 7, 12, 17, 22, ...

    9-27-212-217-2?

  5. 5. Find the 19th term of the arithmetic sequence 22, 27, 32, 37, ...

    19+322+327+332+3?

  6. 6. Find the 20th term of the arithmetic sequence 19, 30, 41, 52, ...

    20-119-130-141-1?

  7. 7. Find the 9th term of the arithmetic sequence 4, 8, 12, 16, ...

    9-54-58-512-5?

  8. 8. Find the 9th term of the arithmetic sequence 9, 12, 15, 18, ...

    9+09+012+015+0?

  9. 9. Find the 21th term of the arithmetic sequence 2, 10, 18, 26, ...

    21-192-1910-1918-19?

  10. 10. Find the 20th term of the arithmetic sequence 25, 37, 49, 61, ...

    20+525+537+549+5?

  11. 11. Find the 21th term of the arithmetic sequence 8, 18, 28, 38, ...

    21-138-1318-1328-13?

  12. 12. Find the 11th term of the arithmetic sequence 10, 22, 34, 46, ...

    11-110-122-134-1?
12 questions · Seed 104730 · 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 16th term of the arithmetic sequence 11, 21, 31, 41, ...

    161

    First term a = 11 and common difference d = 10. Using a + (n − 1)d gives 11 + 15 × 10 = 161.

  2. 2. Find the 12th term of the arithmetic sequence 20, 31, 42, 53, ...

    141

    First term a = 20 and common difference d = 11. Using a + (n − 1)d gives 20 + 11 × 11 = 141.

  3. 3. Find the 17th term of the arithmetic sequence 25, 33, 41, 49, ...

    153

    First term a = 25 and common difference d = 8. Using a + (n − 1)d gives 25 + 16 × 8 = 153.

  4. 4. Find the 9th term of the arithmetic sequence 7, 12, 17, 22, ...

    47

    First term a = 7 and common difference d = 5. Using a + (n − 1)d gives 7 + 8 × 5 = 47.

  5. 5. Find the 19th term of the arithmetic sequence 22, 27, 32, 37, ...

    112

    First term a = 22 and common difference d = 5. Using a + (n − 1)d gives 22 + 18 × 5 = 112.

  6. 6. Find the 20th term of the arithmetic sequence 19, 30, 41, 52, ...

    228

    First term a = 19 and common difference d = 11. Using a + (n − 1)d gives 19 + 19 × 11 = 228.

  7. 7. Find the 9th term of the arithmetic sequence 4, 8, 12, 16, ...

    36

    First term a = 4 and common difference d = 4. Using a + (n − 1)d gives 4 + 8 × 4 = 36.

  8. 8. Find the 9th term of the arithmetic sequence 9, 12, 15, 18, ...

    33

    First term a = 9 and common difference d = 3. Using a + (n − 1)d gives 9 + 8 × 3 = 33.

  9. 9. Find the 21th term of the arithmetic sequence 2, 10, 18, 26, ...

    162

    First term a = 2 and common difference d = 8. Using a + (n − 1)d gives 2 + 20 × 8 = 162.

  10. 10. Find the 20th term of the arithmetic sequence 25, 37, 49, 61, ...

    253

    First term a = 25 and common difference d = 12. Using a + (n − 1)d gives 25 + 19 × 12 = 253.

  11. 11. Find the 21th term of the arithmetic sequence 8, 18, 28, 38, ...

    208

    First term a = 8 and common difference d = 10. Using a + (n − 1)d gives 8 + 20 × 10 = 208.

  12. 12. Find the 11th term of the arithmetic sequence 10, 22, 34, 46, ...

    130

    First term a = 10 and common difference d = 12. Using a + (n − 1)d gives 10 + 10 × 12 = 130.

12 questions · Seed 104730 · 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 16th term of the arithmetic sequence 11, 21, 31, 41, ...

    16-511-521-531-5?

  2. 2. Find the 12th term of the arithmetic sequence 20, 31, 42, 53, ...

    12+820+831+842+8?

  3. 3. Find the 17th term of the arithmetic sequence 25, 33, 41, 49, ...

    17+825+833+841+8?

  4. 4. Find the 9th term of the arithmetic sequence 7, 12, 17, 22, ...

    9-27-212-217-2?

  5. 5. Find the 19th term of the arithmetic sequence 22, 27, 32, 37, ...

    19+322+327+332+3?

  6. 6. Find the 20th term of the arithmetic sequence 19, 30, 41, 52, ...

    20-119-130-141-1?

  7. 7. Find the 9th term of the arithmetic sequence 4, 8, 12, 16, ...

    9-54-58-512-5?

  8. 8. Find the 9th term of the arithmetic sequence 9, 12, 15, 18, ...

    9+09+012+015+0?

  9. 9. Find the 21th term of the arithmetic sequence 2, 10, 18, 26, ...

    21-192-1910-1918-19?

  10. 10. Find the 20th term of the arithmetic sequence 25, 37, 49, 61, ...

    20+525+537+549+5?

  11. 11. Find the 21th term of the arithmetic sequence 8, 18, 28, 38, ...

    21-138-1318-1328-13?

  12. 12. Find the 11th term of the arithmetic sequence 10, 22, 34, 46, ...

    11-110-122-134-1?
12 questions · Seed 104730 · 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 16th term of the arithmetic sequence 11, 21, 31, 41, ...

    161

    First term a = 11 and common difference d = 10. Using a + (n − 1)d gives 11 + 15 × 10 = 161.

  2. 2. Find the 12th term of the arithmetic sequence 20, 31, 42, 53, ...

    141

    First term a = 20 and common difference d = 11. Using a + (n − 1)d gives 20 + 11 × 11 = 141.

  3. 3. Find the 17th term of the arithmetic sequence 25, 33, 41, 49, ...

    153

    First term a = 25 and common difference d = 8. Using a + (n − 1)d gives 25 + 16 × 8 = 153.

  4. 4. Find the 9th term of the arithmetic sequence 7, 12, 17, 22, ...

    47

    First term a = 7 and common difference d = 5. Using a + (n − 1)d gives 7 + 8 × 5 = 47.

  5. 5. Find the 19th term of the arithmetic sequence 22, 27, 32, 37, ...

    112

    First term a = 22 and common difference d = 5. Using a + (n − 1)d gives 22 + 18 × 5 = 112.

  6. 6. Find the 20th term of the arithmetic sequence 19, 30, 41, 52, ...

    228

    First term a = 19 and common difference d = 11. Using a + (n − 1)d gives 19 + 19 × 11 = 228.

  7. 7. Find the 9th term of the arithmetic sequence 4, 8, 12, 16, ...

    36

    First term a = 4 and common difference d = 4. Using a + (n − 1)d gives 4 + 8 × 4 = 36.

  8. 8. Find the 9th term of the arithmetic sequence 9, 12, 15, 18, ...

    33

    First term a = 9 and common difference d = 3. Using a + (n − 1)d gives 9 + 8 × 3 = 33.

  9. 9. Find the 21th term of the arithmetic sequence 2, 10, 18, 26, ...

    162

    First term a = 2 and common difference d = 8. Using a + (n − 1)d gives 2 + 20 × 8 = 162.

  10. 10. Find the 20th term of the arithmetic sequence 25, 37, 49, 61, ...

    253

    First term a = 25 and common difference d = 12. Using a + (n − 1)d gives 25 + 19 × 12 = 253.

  11. 11. Find the 21th term of the arithmetic sequence 8, 18, 28, 38, ...

    208

    First term a = 8 and common difference d = 10. Using a + (n − 1)d gives 8 + 20 × 10 = 208.

  12. 12. Find the 11th term of the arithmetic sequence 10, 22, 34, 46, ...

    130

    First term a = 10 and common difference d = 12. Using a + (n − 1)d gives 10 + 10 × 12 = 130.

12 questions · Seed 104730 · Age guidance, not curriculum certification