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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 25th term of the arithmetic sequence 16, 24, 32, 40, ...

    25-916-924-932-9?

  2. 2. Find the 21th term of the arithmetic sequence 2, 13, 24, 35, ...

    21-192-1913-1924-19?

  3. 3. Find the 8th term of the arithmetic sequence 4, 12, 20, 28, ...

    8-44-412-420-4?

  4. 4. Find the 10th term of the arithmetic sequence 7, 12, 17, 22, ...

    10-37-312-317-3?

  5. 5. Find the 13th term of the arithmetic sequence 25, 31, 37, 43, ...

    13+1225+1231+1237+12?

  6. 6. Find the 22th term of the arithmetic sequence 18, 22, 26, 30, ...

    22-418-422-426-4?

  7. 7. Find the 23th term of the arithmetic sequence 5, 16, 27, 38, ...

    23-185-1816-1827-18?

  8. 8. Find the 8th term of the arithmetic sequence 10, 17, 24, 31, ...

    8+210+217+224+2?

  9. 9. Find the 20th term of the arithmetic sequence 21, 31, 41, 51, ...

    20+121+131+141+1?

  10. 10. Find the 23th term of the arithmetic sequence 25, 28, 31, 34, ...

    23+225+228+231+2?

  11. 11. Find the 10th term of the arithmetic sequence 5, 8, 11, 14, ...

    10-55-58-511-5?

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

    17-314-317-320-3?
12 questions · Seed 104737 · 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 25th term of the arithmetic sequence 16, 24, 32, 40, ...

    208

    First term a = 16 and common difference d = 8. Using a + (n − 1)d gives 16 + 24 × 8 = 208.

  2. 2. Find the 21th term of the arithmetic sequence 2, 13, 24, 35, ...

    222

    First term a = 2 and common difference d = 11. Using a + (n − 1)d gives 2 + 20 × 11 = 222.

  3. 3. Find the 8th term of the arithmetic sequence 4, 12, 20, 28, ...

    60

    First term a = 4 and common difference d = 8. Using a + (n − 1)d gives 4 + 7 × 8 = 60.

  4. 4. Find the 10th term of the arithmetic sequence 7, 12, 17, 22, ...

    52

    First term a = 7 and common difference d = 5. Using a + (n − 1)d gives 7 + 9 × 5 = 52.

  5. 5. Find the 13th term of the arithmetic sequence 25, 31, 37, 43, ...

    97

    First term a = 25 and common difference d = 6. Using a + (n − 1)d gives 25 + 12 × 6 = 97.

  6. 6. Find the 22th term of the arithmetic sequence 18, 22, 26, 30, ...

    102

    First term a = 18 and common difference d = 4. Using a + (n − 1)d gives 18 + 21 × 4 = 102.

  7. 7. Find the 23th term of the arithmetic sequence 5, 16, 27, 38, ...

    247

    First term a = 5 and common difference d = 11. Using a + (n − 1)d gives 5 + 22 × 11 = 247.

  8. 8. Find the 8th term of the arithmetic sequence 10, 17, 24, 31, ...

    59

    First term a = 10 and common difference d = 7. Using a + (n − 1)d gives 10 + 7 × 7 = 59.

  9. 9. Find the 20th term of the arithmetic sequence 21, 31, 41, 51, ...

    211

    First term a = 21 and common difference d = 10. Using a + (n − 1)d gives 21 + 19 × 10 = 211.

  10. 10. Find the 23th term of the arithmetic sequence 25, 28, 31, 34, ...

    91

    First term a = 25 and common difference d = 3. Using a + (n − 1)d gives 25 + 22 × 3 = 91.

  11. 11. Find the 10th term of the arithmetic sequence 5, 8, 11, 14, ...

    32

    First term a = 5 and common difference d = 3. Using a + (n − 1)d gives 5 + 9 × 3 = 32.

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

    62

    First term a = 14 and common difference d = 3. Using a + (n − 1)d gives 14 + 16 × 3 = 62.

12 questions · Seed 104737 · 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 25th term of the arithmetic sequence 16, 24, 32, 40, ...

    25-916-924-932-9?

  2. 2. Find the 21th term of the arithmetic sequence 2, 13, 24, 35, ...

    21-192-1913-1924-19?

  3. 3. Find the 8th term of the arithmetic sequence 4, 12, 20, 28, ...

    8-44-412-420-4?

  4. 4. Find the 10th term of the arithmetic sequence 7, 12, 17, 22, ...

    10-37-312-317-3?

  5. 5. Find the 13th term of the arithmetic sequence 25, 31, 37, 43, ...

    13+1225+1231+1237+12?

  6. 6. Find the 22th term of the arithmetic sequence 18, 22, 26, 30, ...

    22-418-422-426-4?

  7. 7. Find the 23th term of the arithmetic sequence 5, 16, 27, 38, ...

    23-185-1816-1827-18?

  8. 8. Find the 8th term of the arithmetic sequence 10, 17, 24, 31, ...

    8+210+217+224+2?

  9. 9. Find the 20th term of the arithmetic sequence 21, 31, 41, 51, ...

    20+121+131+141+1?

  10. 10. Find the 23th term of the arithmetic sequence 25, 28, 31, 34, ...

    23+225+228+231+2?

  11. 11. Find the 10th term of the arithmetic sequence 5, 8, 11, 14, ...

    10-55-58-511-5?

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

    17-314-317-320-3?
12 questions · Seed 104737 · 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 25th term of the arithmetic sequence 16, 24, 32, 40, ...

    208

    First term a = 16 and common difference d = 8. Using a + (n − 1)d gives 16 + 24 × 8 = 208.

  2. 2. Find the 21th term of the arithmetic sequence 2, 13, 24, 35, ...

    222

    First term a = 2 and common difference d = 11. Using a + (n − 1)d gives 2 + 20 × 11 = 222.

  3. 3. Find the 8th term of the arithmetic sequence 4, 12, 20, 28, ...

    60

    First term a = 4 and common difference d = 8. Using a + (n − 1)d gives 4 + 7 × 8 = 60.

  4. 4. Find the 10th term of the arithmetic sequence 7, 12, 17, 22, ...

    52

    First term a = 7 and common difference d = 5. Using a + (n − 1)d gives 7 + 9 × 5 = 52.

  5. 5. Find the 13th term of the arithmetic sequence 25, 31, 37, 43, ...

    97

    First term a = 25 and common difference d = 6. Using a + (n − 1)d gives 25 + 12 × 6 = 97.

  6. 6. Find the 22th term of the arithmetic sequence 18, 22, 26, 30, ...

    102

    First term a = 18 and common difference d = 4. Using a + (n − 1)d gives 18 + 21 × 4 = 102.

  7. 7. Find the 23th term of the arithmetic sequence 5, 16, 27, 38, ...

    247

    First term a = 5 and common difference d = 11. Using a + (n − 1)d gives 5 + 22 × 11 = 247.

  8. 8. Find the 8th term of the arithmetic sequence 10, 17, 24, 31, ...

    59

    First term a = 10 and common difference d = 7. Using a + (n − 1)d gives 10 + 7 × 7 = 59.

  9. 9. Find the 20th term of the arithmetic sequence 21, 31, 41, 51, ...

    211

    First term a = 21 and common difference d = 10. Using a + (n − 1)d gives 21 + 19 × 10 = 211.

  10. 10. Find the 23th term of the arithmetic sequence 25, 28, 31, 34, ...

    91

    First term a = 25 and common difference d = 3. Using a + (n − 1)d gives 25 + 22 × 3 = 91.

  11. 11. Find the 10th term of the arithmetic sequence 5, 8, 11, 14, ...

    32

    First term a = 5 and common difference d = 3. Using a + (n − 1)d gives 5 + 9 × 3 = 32.

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

    62

    First term a = 14 and common difference d = 3. Using a + (n − 1)d gives 14 + 16 × 3 = 62.

12 questions · Seed 104737 · Age guidance, not curriculum certification