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 13-15 Ages 16-18

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Worksheet StudioPractice pack · Ages 16-18

Linear nth-term sequences

Take your time. Show your thinking.

1. Find the 8th term of the arithmetic sequence 2, 10, 18, 26, ...
2. Find the 17th term of the arithmetic sequence 11, 21, 31, 41, ...
3. Find the 15th term of the arithmetic sequence 25, 36, 47, 58, ...
4. Find the 17th term of the arithmetic sequence 17, 23, 29, 35, ...
5. Find the 17th term of the arithmetic sequence 19, 22, 25, 28, ...
6. Find the 17th term of the arithmetic sequence 16, 22, 28, 34, ...
7. Find the 8th term of the arithmetic sequence 15, 24, 33, 42, ...
8. Find the 20th term of the arithmetic sequence 15, 19, 23, 27, ...
9. Find the 24th term of the arithmetic sequence 25, 33, 41, 49, ...
10. Find the 25th term of the arithmetic sequence 2, 14, 26, 38, ...
11. Find the 9th term of the arithmetic sequence 20, 25, 30, 35, ...
12. Find the 16th term of the arithmetic sequence 16, 23, 30, 37, ...

12 questions · Seed 47 · Age guidance, not curriculum certification

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Worksheet StudioAnswer key · Ages 16-18

Linear nth-term sequences

Answers and reasoning. Review before teaching.

1. 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.
2. Find the 17th term of the arithmetic sequence 11, 21, 31, 41, ...
171
First term a = 11 and common difference d = 10. Using a + (n − 1)d gives 11 + 16 × 10 = 171.
3. Find the 15th term of the arithmetic sequence 25, 36, 47, 58, ...
179
First term a = 25 and common difference d = 11. Using a + (n − 1)d gives 25 + 14 × 11 = 179.
4. Find the 17th term of the arithmetic sequence 17, 23, 29, 35, ...
113
First term a = 17 and common difference d = 6. Using a + (n − 1)d gives 17 + 16 × 6 = 113.
5. Find the 17th term of the arithmetic sequence 19, 22, 25, 28, ...
67
First term a = 19 and common difference d = 3. Using a + (n − 1)d gives 19 + 16 × 3 = 67.
6. Find the 17th term of the arithmetic sequence 16, 22, 28, 34, ...
112
First term a = 16 and common difference d = 6. Using a + (n − 1)d gives 16 + 16 × 6 = 112.
7. Find the 8th term of the arithmetic sequence 15, 24, 33, 42, ...
78
First term a = 15 and common difference d = 9. Using a + (n − 1)d gives 15 + 7 × 9 = 78.
8. Find the 20th term of the arithmetic sequence 15, 19, 23, 27, ...
91
First term a = 15 and common difference d = 4. Using a + (n − 1)d gives 15 + 19 × 4 = 91.
9. Find the 24th term of the arithmetic sequence 25, 33, 41, 49, ...
209
First term a = 25 and common difference d = 8. Using a + (n − 1)d gives 25 + 23 × 8 = 209.
10. Find the 25th term of the arithmetic sequence 2, 14, 26, 38, ...
290
First term a = 2 and common difference d = 12. Using a + (n − 1)d gives 2 + 24 × 12 = 290.
11. Find the 9th term of the arithmetic sequence 20, 25, 30, 35, ...
60
First term a = 20 and common difference d = 5. Using a + (n − 1)d gives 20 + 8 × 5 = 60.
12. Find the 16th term of the arithmetic sequence 16, 23, 30, 37, ...
121
First term a = 16 and common difference d = 7. Using a + (n − 1)d gives 16 + 15 × 7 = 121.

12 questions · Seed 47 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Linear nth-term sequences

Take your time. Show your thinking.

1. Find the 8th term of the arithmetic sequence 2, 10, 18, 26, ...
2. Find the 17th term of the arithmetic sequence 11, 21, 31, 41, ...
3. Find the 15th term of the arithmetic sequence 25, 36, 47, 58, ...
4. Find the 17th term of the arithmetic sequence 17, 23, 29, 35, ...
5. Find the 17th term of the arithmetic sequence 19, 22, 25, 28, ...
6. Find the 17th term of the arithmetic sequence 16, 22, 28, 34, ...
7. Find the 8th term of the arithmetic sequence 15, 24, 33, 42, ...
8. Find the 20th term of the arithmetic sequence 15, 19, 23, 27, ...
9. Find the 24th term of the arithmetic sequence 25, 33, 41, 49, ...
10. Find the 25th term of the arithmetic sequence 2, 14, 26, 38, ...
11. Find the 9th term of the arithmetic sequence 20, 25, 30, 35, ...
12. Find the 16th term of the arithmetic sequence 16, 23, 30, 37, ...

12 questions · Seed 47 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Linear nth-term sequences

Answers and reasoning. Review before teaching.

1. 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.
2. Find the 17th term of the arithmetic sequence 11, 21, 31, 41, ...
171
First term a = 11 and common difference d = 10. Using a + (n − 1)d gives 11 + 16 × 10 = 171.
3. Find the 15th term of the arithmetic sequence 25, 36, 47, 58, ...
179
First term a = 25 and common difference d = 11. Using a + (n − 1)d gives 25 + 14 × 11 = 179.
4. Find the 17th term of the arithmetic sequence 17, 23, 29, 35, ...
113
First term a = 17 and common difference d = 6. Using a + (n − 1)d gives 17 + 16 × 6 = 113.
5. Find the 17th term of the arithmetic sequence 19, 22, 25, 28, ...
67
First term a = 19 and common difference d = 3. Using a + (n − 1)d gives 19 + 16 × 3 = 67.
6. Find the 17th term of the arithmetic sequence 16, 22, 28, 34, ...
112
First term a = 16 and common difference d = 6. Using a + (n − 1)d gives 16 + 16 × 6 = 112.
7. Find the 8th term of the arithmetic sequence 15, 24, 33, 42, ...
78
First term a = 15 and common difference d = 9. Using a + (n − 1)d gives 15 + 7 × 9 = 78.
8. Find the 20th term of the arithmetic sequence 15, 19, 23, 27, ...
91
First term a = 15 and common difference d = 4. Using a + (n − 1)d gives 15 + 19 × 4 = 91.
9. Find the 24th term of the arithmetic sequence 25, 33, 41, 49, ...
209
First term a = 25 and common difference d = 8. Using a + (n − 1)d gives 25 + 23 × 8 = 209.
10. Find the 25th term of the arithmetic sequence 2, 14, 26, 38, ...
290
First term a = 2 and common difference d = 12. Using a + (n − 1)d gives 2 + 24 × 12 = 290.
11. Find the 9th term of the arithmetic sequence 20, 25, 30, 35, ...
60
First term a = 20 and common difference d = 5. Using a + (n − 1)d gives 20 + 8 × 5 = 60.
12. Find the 16th term of the arithmetic sequence 16, 23, 30, 37, ...
121
First term a = 16 and common difference d = 7. Using a + (n − 1)d gives 16 + 15 × 7 = 121.

12 questions · Seed 47 · Age guidance, not curriculum certification