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 23th term of the arithmetic sequence 19, 26, 33, 40, ...
2. Find the 16th term of the arithmetic sequence 24, 34, 44, 54, ...
3. Find the 19th term of the arithmetic sequence 13, 23, 33, 43, ...
4. Find the 14th term of the arithmetic sequence 11, 18, 25, 32, ...
5. Find the 19th term of the arithmetic sequence 2, 4, 6, 8, ...
6. Find the 23th term of the arithmetic sequence 17, 25, 33, 41, ...
7. Find the 20th term of the arithmetic sequence 23, 28, 33, 38, ...
8. Find the 17th term of the arithmetic sequence 19, 26, 33, 40, ...
9. Find the 16th term of the arithmetic sequence 20, 30, 40, 50, ...
10. Find the 17th term of the arithmetic sequence 6, 14, 22, 30, ...
11. Find the 20th term of the arithmetic sequence 10, 13, 16, 19, ...
12. Find the 25th term of the arithmetic sequence 16, 24, 32, 40, ...

12 questions · Seed 42 · 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 23th term of the arithmetic sequence 19, 26, 33, 40, ...
173
First term a = 19 and common difference d = 7. Using a + (n − 1)d gives 19 + 22 × 7 = 173.
2. Find the 16th term of the arithmetic sequence 24, 34, 44, 54, ...
174
First term a = 24 and common difference d = 10. Using a + (n − 1)d gives 24 + 15 × 10 = 174.
3. Find the 19th term of the arithmetic sequence 13, 23, 33, 43, ...
193
First term a = 13 and common difference d = 10. Using a + (n − 1)d gives 13 + 18 × 10 = 193.
4. Find the 14th term of the arithmetic sequence 11, 18, 25, 32, ...
102
First term a = 11 and common difference d = 7. Using a + (n − 1)d gives 11 + 13 × 7 = 102.
5. Find the 19th term of the arithmetic sequence 2, 4, 6, 8, ...
38
First term a = 2 and common difference d = 2. Using a + (n − 1)d gives 2 + 18 × 2 = 38.
6. Find the 23th term of the arithmetic sequence 17, 25, 33, 41, ...
193
First term a = 17 and common difference d = 8. Using a + (n − 1)d gives 17 + 22 × 8 = 193.
7. Find the 20th term of the arithmetic sequence 23, 28, 33, 38, ...
118
First term a = 23 and common difference d = 5. Using a + (n − 1)d gives 23 + 19 × 5 = 118.
8. Find the 17th term of the arithmetic sequence 19, 26, 33, 40, ...
131
First term a = 19 and common difference d = 7. Using a + (n − 1)d gives 19 + 16 × 7 = 131.
9. Find the 16th term of the arithmetic sequence 20, 30, 40, 50, ...
170
First term a = 20 and common difference d = 10. Using a + (n − 1)d gives 20 + 15 × 10 = 170.
10. Find the 17th term of the arithmetic sequence 6, 14, 22, 30, ...
134
First term a = 6 and common difference d = 8. Using a + (n − 1)d gives 6 + 16 × 8 = 134.
11. Find the 20th term of the arithmetic sequence 10, 13, 16, 19, ...
67
First term a = 10 and common difference d = 3. Using a + (n − 1)d gives 10 + 19 × 3 = 67.
12. 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.

12 questions · Seed 42 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Linear nth-term sequences

Take your time. Show your thinking.

1. Find the 23th term of the arithmetic sequence 19, 26, 33, 40, ...
2. Find the 16th term of the arithmetic sequence 24, 34, 44, 54, ...
3. Find the 19th term of the arithmetic sequence 13, 23, 33, 43, ...
4. Find the 14th term of the arithmetic sequence 11, 18, 25, 32, ...
5. Find the 19th term of the arithmetic sequence 2, 4, 6, 8, ...
6. Find the 23th term of the arithmetic sequence 17, 25, 33, 41, ...
7. Find the 20th term of the arithmetic sequence 23, 28, 33, 38, ...
8. Find the 17th term of the arithmetic sequence 19, 26, 33, 40, ...
9. Find the 16th term of the arithmetic sequence 20, 30, 40, 50, ...
10. Find the 17th term of the arithmetic sequence 6, 14, 22, 30, ...
11. Find the 20th term of the arithmetic sequence 10, 13, 16, 19, ...
12. Find the 25th term of the arithmetic sequence 16, 24, 32, 40, ...

12 questions · Seed 42 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Linear nth-term sequences

Answers and reasoning. Review before teaching.

1. Find the 23th term of the arithmetic sequence 19, 26, 33, 40, ...
173
First term a = 19 and common difference d = 7. Using a + (n − 1)d gives 19 + 22 × 7 = 173.
2. Find the 16th term of the arithmetic sequence 24, 34, 44, 54, ...
174
First term a = 24 and common difference d = 10. Using a + (n − 1)d gives 24 + 15 × 10 = 174.
3. Find the 19th term of the arithmetic sequence 13, 23, 33, 43, ...
193
First term a = 13 and common difference d = 10. Using a + (n − 1)d gives 13 + 18 × 10 = 193.
4. Find the 14th term of the arithmetic sequence 11, 18, 25, 32, ...
102
First term a = 11 and common difference d = 7. Using a + (n − 1)d gives 11 + 13 × 7 = 102.
5. Find the 19th term of the arithmetic sequence 2, 4, 6, 8, ...
38
First term a = 2 and common difference d = 2. Using a + (n − 1)d gives 2 + 18 × 2 = 38.
6. Find the 23th term of the arithmetic sequence 17, 25, 33, 41, ...
193
First term a = 17 and common difference d = 8. Using a + (n − 1)d gives 17 + 22 × 8 = 193.
7. Find the 20th term of the arithmetic sequence 23, 28, 33, 38, ...
118
First term a = 23 and common difference d = 5. Using a + (n − 1)d gives 23 + 19 × 5 = 118.
8. Find the 17th term of the arithmetic sequence 19, 26, 33, 40, ...
131
First term a = 19 and common difference d = 7. Using a + (n − 1)d gives 19 + 16 × 7 = 131.
9. Find the 16th term of the arithmetic sequence 20, 30, 40, 50, ...
170
First term a = 20 and common difference d = 10. Using a + (n − 1)d gives 20 + 15 × 10 = 170.
10. Find the 17th term of the arithmetic sequence 6, 14, 22, 30, ...
134
First term a = 6 and common difference d = 8. Using a + (n − 1)d gives 6 + 16 × 8 = 134.
11. Find the 20th term of the arithmetic sequence 10, 13, 16, 19, ...
67
First term a = 10 and common difference d = 3. Using a + (n − 1)d gives 10 + 19 × 3 = 67.
12. 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.

12 questions · Seed 42 · Age guidance, not curriculum certification