Small practice. Bright discoveries.Explore the free starter collection
worksheetstudio.
Sign in
Back to worksheets
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.

New variationTry interactive challengeBrowse templates
Age band:Ages 13-15Ages 16-18

Choose “Save as PDF” to keep a copy. Use your browser’s paper setting for A4 or Letter.

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 17, 24, 31, 38, ...

    25-817-824-831-8?

  2. 2. Find the 22th term of the arithmetic sequence 5, 17, 29, 41, ...

    22-175-1717-1729-17?

  3. 3. Find the 16th term of the arithmetic sequence 17, 19, 21, 23, ...

    16+117+119+121+1?

  4. 4. Find the 15th term of the arithmetic sequence 10, 17, 24, 31, ...

    15-510-517-524-5?

  5. 5. Find the 22th term of the arithmetic sequence 13, 25, 37, 49, ...

    22-913-925-937-9?

  6. 6. Find the 23th term of the arithmetic sequence 24, 35, 46, 57, ...

    23+124+135+146+1?

  7. 7. Find the 14th term of the arithmetic sequence 7, 12, 17, 22, ...

    14-77-712-717-7?

  8. 8. Find the 21th term of the arithmetic sequence 14, 16, 18, 20, ...

    21-714-716-718-7?

  9. 9. Find the 13th term of the arithmetic sequence 24, 31, 38, 45, ...

    13+1124+1131+1138+11?

  10. 10. Find the 15th term of the arithmetic sequence 24, 34, 44, 54, ...

    15+924+934+944+9?

  11. 11. Find the 23th term of the arithmetic sequence 7, 9, 11, 13, ...

    23-167-169-1611-16?

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

    9-27-212-217-2?
12 questions · Seed 104734 · 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 17, 24, 31, 38, ...

    185

    First term a = 17 and common difference d = 7. Using a + (n − 1)d gives 17 + 24 × 7 = 185.

  2. 2. Find the 22th term of the arithmetic sequence 5, 17, 29, 41, ...

    257

    First term a = 5 and common difference d = 12. Using a + (n − 1)d gives 5 + 21 × 12 = 257.

  3. 3. Find the 16th term of the arithmetic sequence 17, 19, 21, 23, ...

    47

    First term a = 17 and common difference d = 2. Using a + (n − 1)d gives 17 + 15 × 2 = 47.

  4. 4. Find the 15th term of the arithmetic sequence 10, 17, 24, 31, ...

    108

    First term a = 10 and common difference d = 7. Using a + (n − 1)d gives 10 + 14 × 7 = 108.

  5. 5. Find the 22th term of the arithmetic sequence 13, 25, 37, 49, ...

    265

    First term a = 13 and common difference d = 12. Using a + (n − 1)d gives 13 + 21 × 12 = 265.

  6. 6. Find the 23th term of the arithmetic sequence 24, 35, 46, 57, ...

    266

    First term a = 24 and common difference d = 11. Using a + (n − 1)d gives 24 + 22 × 11 = 266.

  7. 7. Find the 14th term of the arithmetic sequence 7, 12, 17, 22, ...

    72

    First term a = 7 and common difference d = 5. Using a + (n − 1)d gives 7 + 13 × 5 = 72.

  8. 8. Find the 21th term of the arithmetic sequence 14, 16, 18, 20, ...

    54

    First term a = 14 and common difference d = 2. Using a + (n − 1)d gives 14 + 20 × 2 = 54.

  9. 9. Find the 13th term of the arithmetic sequence 24, 31, 38, 45, ...

    108

    First term a = 24 and common difference d = 7. Using a + (n − 1)d gives 24 + 12 × 7 = 108.

  10. 10. Find the 15th term of the arithmetic sequence 24, 34, 44, 54, ...

    164

    First term a = 24 and common difference d = 10. Using a + (n − 1)d gives 24 + 14 × 10 = 164.

  11. 11. Find the 23th term of the arithmetic sequence 7, 9, 11, 13, ...

    51

    First term a = 7 and common difference d = 2. Using a + (n − 1)d gives 7 + 22 × 2 = 51.

  12. 12. 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.

12 questions · Seed 104734 · 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 17, 24, 31, 38, ...

    25-817-824-831-8?

  2. 2. Find the 22th term of the arithmetic sequence 5, 17, 29, 41, ...

    22-175-1717-1729-17?

  3. 3. Find the 16th term of the arithmetic sequence 17, 19, 21, 23, ...

    16+117+119+121+1?

  4. 4. Find the 15th term of the arithmetic sequence 10, 17, 24, 31, ...

    15-510-517-524-5?

  5. 5. Find the 22th term of the arithmetic sequence 13, 25, 37, 49, ...

    22-913-925-937-9?

  6. 6. Find the 23th term of the arithmetic sequence 24, 35, 46, 57, ...

    23+124+135+146+1?

  7. 7. Find the 14th term of the arithmetic sequence 7, 12, 17, 22, ...

    14-77-712-717-7?

  8. 8. Find the 21th term of the arithmetic sequence 14, 16, 18, 20, ...

    21-714-716-718-7?

  9. 9. Find the 13th term of the arithmetic sequence 24, 31, 38, 45, ...

    13+1124+1131+1138+11?

  10. 10. Find the 15th term of the arithmetic sequence 24, 34, 44, 54, ...

    15+924+934+944+9?

  11. 11. Find the 23th term of the arithmetic sequence 7, 9, 11, 13, ...

    23-167-169-1611-16?

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

    9-27-212-217-2?
12 questions · Seed 104734 · 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 17, 24, 31, 38, ...

    185

    First term a = 17 and common difference d = 7. Using a + (n − 1)d gives 17 + 24 × 7 = 185.

  2. 2. Find the 22th term of the arithmetic sequence 5, 17, 29, 41, ...

    257

    First term a = 5 and common difference d = 12. Using a + (n − 1)d gives 5 + 21 × 12 = 257.

  3. 3. Find the 16th term of the arithmetic sequence 17, 19, 21, 23, ...

    47

    First term a = 17 and common difference d = 2. Using a + (n − 1)d gives 17 + 15 × 2 = 47.

  4. 4. Find the 15th term of the arithmetic sequence 10, 17, 24, 31, ...

    108

    First term a = 10 and common difference d = 7. Using a + (n − 1)d gives 10 + 14 × 7 = 108.

  5. 5. Find the 22th term of the arithmetic sequence 13, 25, 37, 49, ...

    265

    First term a = 13 and common difference d = 12. Using a + (n − 1)d gives 13 + 21 × 12 = 265.

  6. 6. Find the 23th term of the arithmetic sequence 24, 35, 46, 57, ...

    266

    First term a = 24 and common difference d = 11. Using a + (n − 1)d gives 24 + 22 × 11 = 266.

  7. 7. Find the 14th term of the arithmetic sequence 7, 12, 17, 22, ...

    72

    First term a = 7 and common difference d = 5. Using a + (n − 1)d gives 7 + 13 × 5 = 72.

  8. 8. Find the 21th term of the arithmetic sequence 14, 16, 18, 20, ...

    54

    First term a = 14 and common difference d = 2. Using a + (n − 1)d gives 14 + 20 × 2 = 54.

  9. 9. Find the 13th term of the arithmetic sequence 24, 31, 38, 45, ...

    108

    First term a = 24 and common difference d = 7. Using a + (n − 1)d gives 24 + 12 × 7 = 108.

  10. 10. Find the 15th term of the arithmetic sequence 24, 34, 44, 54, ...

    164

    First term a = 24 and common difference d = 10. Using a + (n − 1)d gives 24 + 14 × 10 = 164.

  11. 11. Find the 23th term of the arithmetic sequence 7, 9, 11, 13, ...

    51

    First term a = 7 and common difference d = 2. Using a + (n − 1)d gives 7 + 22 × 2 = 51.

  12. 12. 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.

12 questions · Seed 104734 · Age guidance, not curriculum certification