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 variation Try interactive challenge Browse templates

Age band:Ages 13-15 Ages 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. Find the 15th term of the arithmetic sequence 24, 30, 36, 42, ...
2. Find the 12th term of the arithmetic sequence 21, 24, 27, 30, ...
3. Find the 23th term of the arithmetic sequence 3, 10, 17, 24, ...
4. Find the 10th term of the arithmetic sequence 25, 30, 35, 40, ...
5. Find the 17th term of the arithmetic sequence 22, 29, 36, 43, ...
6. Find the 15th term of the arithmetic sequence 2, 13, 24, 35, ...
7. Find the 25th term of the arithmetic sequence 13, 21, 29, 37, ...
8. Find the 22th term of the arithmetic sequence 20, 22, 24, 26, ...
9. Find the 17th term of the arithmetic sequence 6, 11, 16, 21, ...
10. Find the 17th term of the arithmetic sequence 15, 17, 19, 21, ...
11. Find the 8th term of the arithmetic sequence 22, 31, 40, 49, ...
12. Find the 21th term of the arithmetic sequence 15, 18, 21, 24, ...

12 questions · Seed 60 · 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. Find the 15th term of the arithmetic sequence 24, 30, 36, 42, ...
108
First term a = 24 and common difference d = 6. Using a + (n − 1)d gives 24 + 14 × 6 = 108.
2. Find the 12th term of the arithmetic sequence 21, 24, 27, 30, ...
54
First term a = 21 and common difference d = 3. Using a + (n − 1)d gives 21 + 11 × 3 = 54.
3. Find the 23th term of the arithmetic sequence 3, 10, 17, 24, ...
157
First term a = 3 and common difference d = 7. Using a + (n − 1)d gives 3 + 22 × 7 = 157.
4. Find the 10th term of the arithmetic sequence 25, 30, 35, 40, ...
70
First term a = 25 and common difference d = 5. Using a + (n − 1)d gives 25 + 9 × 5 = 70.
5. Find the 17th term of the arithmetic sequence 22, 29, 36, 43, ...
134
First term a = 22 and common difference d = 7. Using a + (n − 1)d gives 22 + 16 × 7 = 134.
6. Find the 15th term of the arithmetic sequence 2, 13, 24, 35, ...
156
First term a = 2 and common difference d = 11. Using a + (n − 1)d gives 2 + 14 × 11 = 156.
7. Find the 25th term of the arithmetic sequence 13, 21, 29, 37, ...
205
First term a = 13 and common difference d = 8. Using a + (n − 1)d gives 13 + 24 × 8 = 205.
8. Find the 22th term of the arithmetic sequence 20, 22, 24, 26, ...
62
First term a = 20 and common difference d = 2. Using a + (n − 1)d gives 20 + 21 × 2 = 62.
9. Find the 17th term of the arithmetic sequence 6, 11, 16, 21, ...
86
First term a = 6 and common difference d = 5. Using a + (n − 1)d gives 6 + 16 × 5 = 86.
10. Find the 17th term of the arithmetic sequence 15, 17, 19, 21, ...
47
First term a = 15 and common difference d = 2. Using a + (n − 1)d gives 15 + 16 × 2 = 47.
11. Find the 8th term of the arithmetic sequence 22, 31, 40, 49, ...
85
First term a = 22 and common difference d = 9. Using a + (n − 1)d gives 22 + 7 × 9 = 85.
12. Find the 21th term of the arithmetic sequence 15, 18, 21, 24, ...
75
First term a = 15 and common difference d = 3. Using a + (n − 1)d gives 15 + 20 × 3 = 75.

12 questions · Seed 60 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Linear nth-term sequences

Take your time. Show your thinking.

1. Find the 15th term of the arithmetic sequence 24, 30, 36, 42, ...
2. Find the 12th term of the arithmetic sequence 21, 24, 27, 30, ...
3. Find the 23th term of the arithmetic sequence 3, 10, 17, 24, ...
4. Find the 10th term of the arithmetic sequence 25, 30, 35, 40, ...
5. Find the 17th term of the arithmetic sequence 22, 29, 36, 43, ...
6. Find the 15th term of the arithmetic sequence 2, 13, 24, 35, ...
7. Find the 25th term of the arithmetic sequence 13, 21, 29, 37, ...
8. Find the 22th term of the arithmetic sequence 20, 22, 24, 26, ...
9. Find the 17th term of the arithmetic sequence 6, 11, 16, 21, ...
10. Find the 17th term of the arithmetic sequence 15, 17, 19, 21, ...
11. Find the 8th term of the arithmetic sequence 22, 31, 40, 49, ...
12. Find the 21th term of the arithmetic sequence 15, 18, 21, 24, ...

12 questions · Seed 60 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Linear nth-term sequences

Answers and reasoning. Review before teaching.

1. Find the 15th term of the arithmetic sequence 24, 30, 36, 42, ...
108
First term a = 24 and common difference d = 6. Using a + (n − 1)d gives 24 + 14 × 6 = 108.
2. Find the 12th term of the arithmetic sequence 21, 24, 27, 30, ...
54
First term a = 21 and common difference d = 3. Using a + (n − 1)d gives 21 + 11 × 3 = 54.
3. Find the 23th term of the arithmetic sequence 3, 10, 17, 24, ...
157
First term a = 3 and common difference d = 7. Using a + (n − 1)d gives 3 + 22 × 7 = 157.
4. Find the 10th term of the arithmetic sequence 25, 30, 35, 40, ...
70
First term a = 25 and common difference d = 5. Using a + (n − 1)d gives 25 + 9 × 5 = 70.
5. Find the 17th term of the arithmetic sequence 22, 29, 36, 43, ...
134
First term a = 22 and common difference d = 7. Using a + (n − 1)d gives 22 + 16 × 7 = 134.
6. Find the 15th term of the arithmetic sequence 2, 13, 24, 35, ...
156
First term a = 2 and common difference d = 11. Using a + (n − 1)d gives 2 + 14 × 11 = 156.
7. Find the 25th term of the arithmetic sequence 13, 21, 29, 37, ...
205
First term a = 13 and common difference d = 8. Using a + (n − 1)d gives 13 + 24 × 8 = 205.
8. Find the 22th term of the arithmetic sequence 20, 22, 24, 26, ...
62
First term a = 20 and common difference d = 2. Using a + (n − 1)d gives 20 + 21 × 2 = 62.
9. Find the 17th term of the arithmetic sequence 6, 11, 16, 21, ...
86
First term a = 6 and common difference d = 5. Using a + (n − 1)d gives 6 + 16 × 5 = 86.
10. Find the 17th term of the arithmetic sequence 15, 17, 19, 21, ...
47
First term a = 15 and common difference d = 2. Using a + (n − 1)d gives 15 + 16 × 2 = 47.
11. Find the 8th term of the arithmetic sequence 22, 31, 40, 49, ...
85
First term a = 22 and common difference d = 9. Using a + (n − 1)d gives 22 + 7 × 9 = 85.
12. Find the 21th term of the arithmetic sequence 15, 18, 21, 24, ...
75
First term a = 15 and common difference d = 3. Using a + (n − 1)d gives 15 + 20 × 3 = 75.

12 questions · Seed 60 · Age guidance, not curriculum certification