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 9th term of the arithmetic sequence 14, 18, 22, 26, ...
2. Find the 12th term of the arithmetic sequence 2, 9, 16, 23, ...
3. Find the 14th term of the arithmetic sequence 6, 12, 18, 24, ...
4. Find the 19th term of the arithmetic sequence 11, 23, 35, 47, ...
5. Find the 24th term of the arithmetic sequence 15, 20, 25, 30, ...
6. Find the 19th term of the arithmetic sequence 21, 32, 43, 54, ...
7. Find the 24th term of the arithmetic sequence 8, 10, 12, 14, ...
8. Find the 15th term of the arithmetic sequence 25, 32, 39, 46, ...
9. Find the 13th term of the arithmetic sequence 12, 22, 32, 42, ...
10. Find the 11th term of the arithmetic sequence 5, 17, 29, 41, ...
11. Find the 10th term of the arithmetic sequence 12, 15, 18, 21, ...
12. Find the 13th term of the arithmetic sequence 21, 24, 27, 30, ...

12 questions · Seed 53 · 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 9th term of the arithmetic sequence 14, 18, 22, 26, ...
46
First term a = 14 and common difference d = 4. Using a + (n − 1)d gives 14 + 8 × 4 = 46.
2. Find the 12th term of the arithmetic sequence 2, 9, 16, 23, ...
79
First term a = 2 and common difference d = 7. Using a + (n − 1)d gives 2 + 11 × 7 = 79.
3. Find the 14th term of the arithmetic sequence 6, 12, 18, 24, ...
84
First term a = 6 and common difference d = 6. Using a + (n − 1)d gives 6 + 13 × 6 = 84.
4. Find the 19th term of the arithmetic sequence 11, 23, 35, 47, ...
227
First term a = 11 and common difference d = 12. Using a + (n − 1)d gives 11 + 18 × 12 = 227.
5. Find the 24th term of the arithmetic sequence 15, 20, 25, 30, ...
130
First term a = 15 and common difference d = 5. Using a + (n − 1)d gives 15 + 23 × 5 = 130.
6. Find the 19th term of the arithmetic sequence 21, 32, 43, 54, ...
219
First term a = 21 and common difference d = 11. Using a + (n − 1)d gives 21 + 18 × 11 = 219.
7. Find the 24th term of the arithmetic sequence 8, 10, 12, 14, ...
54
First term a = 8 and common difference d = 2. Using a + (n − 1)d gives 8 + 23 × 2 = 54.
8. Find the 15th term of the arithmetic sequence 25, 32, 39, 46, ...
123
First term a = 25 and common difference d = 7. Using a + (n − 1)d gives 25 + 14 × 7 = 123.
9. Find the 13th term of the arithmetic sequence 12, 22, 32, 42, ...
132
First term a = 12 and common difference d = 10. Using a + (n − 1)d gives 12 + 12 × 10 = 132.
10. Find the 11th term of the arithmetic sequence 5, 17, 29, 41, ...
125
First term a = 5 and common difference d = 12. Using a + (n − 1)d gives 5 + 10 × 12 = 125.
11. Find the 10th term of the arithmetic sequence 12, 15, 18, 21, ...
39
First term a = 12 and common difference d = 3. Using a + (n − 1)d gives 12 + 9 × 3 = 39.
12. Find the 13th term of the arithmetic sequence 21, 24, 27, 30, ...
57
First term a = 21 and common difference d = 3. Using a + (n − 1)d gives 21 + 12 × 3 = 57.

12 questions · Seed 53 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Linear nth-term sequences

Take your time. Show your thinking.

1. Find the 9th term of the arithmetic sequence 14, 18, 22, 26, ...
2. Find the 12th term of the arithmetic sequence 2, 9, 16, 23, ...
3. Find the 14th term of the arithmetic sequence 6, 12, 18, 24, ...
4. Find the 19th term of the arithmetic sequence 11, 23, 35, 47, ...
5. Find the 24th term of the arithmetic sequence 15, 20, 25, 30, ...
6. Find the 19th term of the arithmetic sequence 21, 32, 43, 54, ...
7. Find the 24th term of the arithmetic sequence 8, 10, 12, 14, ...
8. Find the 15th term of the arithmetic sequence 25, 32, 39, 46, ...
9. Find the 13th term of the arithmetic sequence 12, 22, 32, 42, ...
10. Find the 11th term of the arithmetic sequence 5, 17, 29, 41, ...
11. Find the 10th term of the arithmetic sequence 12, 15, 18, 21, ...
12. Find the 13th term of the arithmetic sequence 21, 24, 27, 30, ...

12 questions · Seed 53 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Linear nth-term sequences

Answers and reasoning. Review before teaching.

1. Find the 9th term of the arithmetic sequence 14, 18, 22, 26, ...
46
First term a = 14 and common difference d = 4. Using a + (n − 1)d gives 14 + 8 × 4 = 46.
2. Find the 12th term of the arithmetic sequence 2, 9, 16, 23, ...
79
First term a = 2 and common difference d = 7. Using a + (n − 1)d gives 2 + 11 × 7 = 79.
3. Find the 14th term of the arithmetic sequence 6, 12, 18, 24, ...
84
First term a = 6 and common difference d = 6. Using a + (n − 1)d gives 6 + 13 × 6 = 84.
4. Find the 19th term of the arithmetic sequence 11, 23, 35, 47, ...
227
First term a = 11 and common difference d = 12. Using a + (n − 1)d gives 11 + 18 × 12 = 227.
5. Find the 24th term of the arithmetic sequence 15, 20, 25, 30, ...
130
First term a = 15 and common difference d = 5. Using a + (n − 1)d gives 15 + 23 × 5 = 130.
6. Find the 19th term of the arithmetic sequence 21, 32, 43, 54, ...
219
First term a = 21 and common difference d = 11. Using a + (n − 1)d gives 21 + 18 × 11 = 219.
7. Find the 24th term of the arithmetic sequence 8, 10, 12, 14, ...
54
First term a = 8 and common difference d = 2. Using a + (n − 1)d gives 8 + 23 × 2 = 54.
8. Find the 15th term of the arithmetic sequence 25, 32, 39, 46, ...
123
First term a = 25 and common difference d = 7. Using a + (n − 1)d gives 25 + 14 × 7 = 123.
9. Find the 13th term of the arithmetic sequence 12, 22, 32, 42, ...
132
First term a = 12 and common difference d = 10. Using a + (n − 1)d gives 12 + 12 × 10 = 132.
10. Find the 11th term of the arithmetic sequence 5, 17, 29, 41, ...
125
First term a = 5 and common difference d = 12. Using a + (n − 1)d gives 5 + 10 × 12 = 125.
11. Find the 10th term of the arithmetic sequence 12, 15, 18, 21, ...
39
First term a = 12 and common difference d = 3. Using a + (n − 1)d gives 12 + 9 × 3 = 39.
12. Find the 13th term of the arithmetic sequence 21, 24, 27, 30, ...
57
First term a = 21 and common difference d = 3. Using a + (n − 1)d gives 21 + 12 × 3 = 57.

12 questions · Seed 53 · Age guidance, not curriculum certification