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 12th term of the arithmetic sequence 22, 27, 32, 37, ...
2. Find the 13th term of the arithmetic sequence 13, 20, 27, 34, ...
3. Find the 10th term of the arithmetic sequence 18, 25, 32, 39, ...
4. Find the 21th term of the arithmetic sequence 17, 28, 39, 50, ...
5. Find the 22th term of the arithmetic sequence 9, 15, 21, 27, ...
6. Find the 13th term of the arithmetic sequence 19, 28, 37, 46, ...
7. Find the 12th term of the arithmetic sequence 24, 30, 36, 42, ...
8. Find the 19th term of the arithmetic sequence 21, 25, 29, 33, ...
9. Find the 22th term of the arithmetic sequence 17, 25, 33, 41, ...
10. Find the 19th term of the arithmetic sequence 25, 30, 35, 40, ...
11. Find the 17th term of the arithmetic sequence 22, 26, 30, 34, ...
12. Find the 22th term of the arithmetic sequence 21, 23, 25, 27, ...

12 questions · Seed 58 · 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 12th term of the arithmetic sequence 22, 27, 32, 37, ...
77
First term a = 22 and common difference d = 5. Using a + (n − 1)d gives 22 + 11 × 5 = 77.
2. Find the 13th term of the arithmetic sequence 13, 20, 27, 34, ...
97
First term a = 13 and common difference d = 7. Using a + (n − 1)d gives 13 + 12 × 7 = 97.
3. Find the 10th term of the arithmetic sequence 18, 25, 32, 39, ...
81
First term a = 18 and common difference d = 7. Using a + (n − 1)d gives 18 + 9 × 7 = 81.
4. Find the 21th term of the arithmetic sequence 17, 28, 39, 50, ...
237
First term a = 17 and common difference d = 11. Using a + (n − 1)d gives 17 + 20 × 11 = 237.
5. Find the 22th term of the arithmetic sequence 9, 15, 21, 27, ...
135
First term a = 9 and common difference d = 6. Using a + (n − 1)d gives 9 + 21 × 6 = 135.
6. Find the 13th term of the arithmetic sequence 19, 28, 37, 46, ...
127
First term a = 19 and common difference d = 9. Using a + (n − 1)d gives 19 + 12 × 9 = 127.
7. Find the 12th term of the arithmetic sequence 24, 30, 36, 42, ...
90
First term a = 24 and common difference d = 6. Using a + (n − 1)d gives 24 + 11 × 6 = 90.
8. Find the 19th term of the arithmetic sequence 21, 25, 29, 33, ...
93
First term a = 21 and common difference d = 4. Using a + (n − 1)d gives 21 + 18 × 4 = 93.
9. Find the 22th term of the arithmetic sequence 17, 25, 33, 41, ...
185
First term a = 17 and common difference d = 8. Using a + (n − 1)d gives 17 + 21 × 8 = 185.
10. Find the 19th term of the arithmetic sequence 25, 30, 35, 40, ...
115
First term a = 25 and common difference d = 5. Using a + (n − 1)d gives 25 + 18 × 5 = 115.
11. Find the 17th term of the arithmetic sequence 22, 26, 30, 34, ...
86
First term a = 22 and common difference d = 4. Using a + (n − 1)d gives 22 + 16 × 4 = 86.
12. Find the 22th term of the arithmetic sequence 21, 23, 25, 27, ...
63
First term a = 21 and common difference d = 2. Using a + (n − 1)d gives 21 + 21 × 2 = 63.

12 questions · Seed 58 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Linear nth-term sequences

Take your time. Show your thinking.

1. Find the 12th term of the arithmetic sequence 22, 27, 32, 37, ...
2. Find the 13th term of the arithmetic sequence 13, 20, 27, 34, ...
3. Find the 10th term of the arithmetic sequence 18, 25, 32, 39, ...
4. Find the 21th term of the arithmetic sequence 17, 28, 39, 50, ...
5. Find the 22th term of the arithmetic sequence 9, 15, 21, 27, ...
6. Find the 13th term of the arithmetic sequence 19, 28, 37, 46, ...
7. Find the 12th term of the arithmetic sequence 24, 30, 36, 42, ...
8. Find the 19th term of the arithmetic sequence 21, 25, 29, 33, ...
9. Find the 22th term of the arithmetic sequence 17, 25, 33, 41, ...
10. Find the 19th term of the arithmetic sequence 25, 30, 35, 40, ...
11. Find the 17th term of the arithmetic sequence 22, 26, 30, 34, ...
12. Find the 22th term of the arithmetic sequence 21, 23, 25, 27, ...

12 questions · Seed 58 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Linear nth-term sequences

Answers and reasoning. Review before teaching.

1. Find the 12th term of the arithmetic sequence 22, 27, 32, 37, ...
77
First term a = 22 and common difference d = 5. Using a + (n − 1)d gives 22 + 11 × 5 = 77.
2. Find the 13th term of the arithmetic sequence 13, 20, 27, 34, ...
97
First term a = 13 and common difference d = 7. Using a + (n − 1)d gives 13 + 12 × 7 = 97.
3. Find the 10th term of the arithmetic sequence 18, 25, 32, 39, ...
81
First term a = 18 and common difference d = 7. Using a + (n − 1)d gives 18 + 9 × 7 = 81.
4. Find the 21th term of the arithmetic sequence 17, 28, 39, 50, ...
237
First term a = 17 and common difference d = 11. Using a + (n − 1)d gives 17 + 20 × 11 = 237.
5. Find the 22th term of the arithmetic sequence 9, 15, 21, 27, ...
135
First term a = 9 and common difference d = 6. Using a + (n − 1)d gives 9 + 21 × 6 = 135.
6. Find the 13th term of the arithmetic sequence 19, 28, 37, 46, ...
127
First term a = 19 and common difference d = 9. Using a + (n − 1)d gives 19 + 12 × 9 = 127.
7. Find the 12th term of the arithmetic sequence 24, 30, 36, 42, ...
90
First term a = 24 and common difference d = 6. Using a + (n − 1)d gives 24 + 11 × 6 = 90.
8. Find the 19th term of the arithmetic sequence 21, 25, 29, 33, ...
93
First term a = 21 and common difference d = 4. Using a + (n − 1)d gives 21 + 18 × 4 = 93.
9. Find the 22th term of the arithmetic sequence 17, 25, 33, 41, ...
185
First term a = 17 and common difference d = 8. Using a + (n − 1)d gives 17 + 21 × 8 = 185.
10. Find the 19th term of the arithmetic sequence 25, 30, 35, 40, ...
115
First term a = 25 and common difference d = 5. Using a + (n − 1)d gives 25 + 18 × 5 = 115.
11. Find the 17th term of the arithmetic sequence 22, 26, 30, 34, ...
86
First term a = 22 and common difference d = 4. Using a + (n − 1)d gives 22 + 16 × 4 = 86.
12. Find the 22th term of the arithmetic sequence 21, 23, 25, 27, ...
63
First term a = 21 and common difference d = 2. Using a + (n − 1)d gives 21 + 21 × 2 = 63.

12 questions · Seed 58 · Age guidance, not curriculum certification