ReasoningAges 13-15

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 13-15

Linear nth-term sequences

Take your time. Show your thinking.

1. Find the 12th term of the arithmetic sequence 11, 19, 27, 35, ...
2. Find the 17th term of the arithmetic sequence 13, 16, 19, 22, ...
3. Find the 24th term of the arithmetic sequence 10, 16, 22, 28, ...
4. Find the 9th term of the arithmetic sequence 10, 22, 34, 46, ...
5. Find the 8th term of the arithmetic sequence 13, 16, 19, 22, ...
6. Find the 10th term of the arithmetic sequence 6, 14, 22, 30, ...
7. Find the 25th term of the arithmetic sequence 6, 18, 30, 42, ...
8. Find the 23th term of the arithmetic sequence 8, 13, 18, 23, ...
9. Find the 24th term of the arithmetic sequence 14, 25, 36, 47, ...
10. Find the 19th term of the arithmetic sequence 22, 33, 44, 55, ...
11. Find the 18th term of the arithmetic sequence 2, 9, 16, 23, ...
12. Find the 19th term of the arithmetic sequence 9, 15, 21, 27, ...

12 questions · Seed 49 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 13-15

Linear nth-term sequences

Answers and reasoning. Review before teaching.

1. Find the 12th term of the arithmetic sequence 11, 19, 27, 35, ...
99
First term a = 11 and common difference d = 8. Using a + (n − 1)d gives 11 + 11 × 8 = 99.
2. Find the 17th term of the arithmetic sequence 13, 16, 19, 22, ...
61
First term a = 13 and common difference d = 3. Using a + (n − 1)d gives 13 + 16 × 3 = 61.
3. Find the 24th term of the arithmetic sequence 10, 16, 22, 28, ...
148
First term a = 10 and common difference d = 6. Using a + (n − 1)d gives 10 + 23 × 6 = 148.
4. Find the 9th term of the arithmetic sequence 10, 22, 34, 46, ...
106
First term a = 10 and common difference d = 12. Using a + (n − 1)d gives 10 + 8 × 12 = 106.
5. Find the 8th term of the arithmetic sequence 13, 16, 19, 22, ...
34
First term a = 13 and common difference d = 3. Using a + (n − 1)d gives 13 + 7 × 3 = 34.
6. Find the 10th term of the arithmetic sequence 6, 14, 22, 30, ...
78
First term a = 6 and common difference d = 8. Using a + (n − 1)d gives 6 + 9 × 8 = 78.
7. Find the 25th term of the arithmetic sequence 6, 18, 30, 42, ...
294
First term a = 6 and common difference d = 12. Using a + (n − 1)d gives 6 + 24 × 12 = 294.
8. Find the 23th term of the arithmetic sequence 8, 13, 18, 23, ...
118
First term a = 8 and common difference d = 5. Using a + (n − 1)d gives 8 + 22 × 5 = 118.
9. Find the 24th term of the arithmetic sequence 14, 25, 36, 47, ...
267
First term a = 14 and common difference d = 11. Using a + (n − 1)d gives 14 + 23 × 11 = 267.
10. Find the 19th term of the arithmetic sequence 22, 33, 44, 55, ...
220
First term a = 22 and common difference d = 11. Using a + (n − 1)d gives 22 + 18 × 11 = 220.
11. Find the 18th term of the arithmetic sequence 2, 9, 16, 23, ...
121
First term a = 2 and common difference d = 7. Using a + (n − 1)d gives 2 + 17 × 7 = 121.
12. Find the 19th term of the arithmetic sequence 9, 15, 21, 27, ...
117
First term a = 9 and common difference d = 6. Using a + (n − 1)d gives 9 + 18 × 6 = 117.

12 questions · Seed 49 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Linear nth-term sequences

Take your time. Show your thinking.

1. Find the 12th term of the arithmetic sequence 11, 19, 27, 35, ...
2. Find the 17th term of the arithmetic sequence 13, 16, 19, 22, ...
3. Find the 24th term of the arithmetic sequence 10, 16, 22, 28, ...
4. Find the 9th term of the arithmetic sequence 10, 22, 34, 46, ...
5. Find the 8th term of the arithmetic sequence 13, 16, 19, 22, ...
6. Find the 10th term of the arithmetic sequence 6, 14, 22, 30, ...
7. Find the 25th term of the arithmetic sequence 6, 18, 30, 42, ...
8. Find the 23th term of the arithmetic sequence 8, 13, 18, 23, ...
9. Find the 24th term of the arithmetic sequence 14, 25, 36, 47, ...
10. Find the 19th term of the arithmetic sequence 22, 33, 44, 55, ...
11. Find the 18th term of the arithmetic sequence 2, 9, 16, 23, ...
12. Find the 19th term of the arithmetic sequence 9, 15, 21, 27, ...

12 questions · Seed 49 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Linear nth-term sequences

Answers and reasoning. Review before teaching.

1. Find the 12th term of the arithmetic sequence 11, 19, 27, 35, ...
99
First term a = 11 and common difference d = 8. Using a + (n − 1)d gives 11 + 11 × 8 = 99.
2. Find the 17th term of the arithmetic sequence 13, 16, 19, 22, ...
61
First term a = 13 and common difference d = 3. Using a + (n − 1)d gives 13 + 16 × 3 = 61.
3. Find the 24th term of the arithmetic sequence 10, 16, 22, 28, ...
148
First term a = 10 and common difference d = 6. Using a + (n − 1)d gives 10 + 23 × 6 = 148.
4. Find the 9th term of the arithmetic sequence 10, 22, 34, 46, ...
106
First term a = 10 and common difference d = 12. Using a + (n − 1)d gives 10 + 8 × 12 = 106.
5. Find the 8th term of the arithmetic sequence 13, 16, 19, 22, ...
34
First term a = 13 and common difference d = 3. Using a + (n − 1)d gives 13 + 7 × 3 = 34.
6. Find the 10th term of the arithmetic sequence 6, 14, 22, 30, ...
78
First term a = 6 and common difference d = 8. Using a + (n − 1)d gives 6 + 9 × 8 = 78.
7. Find the 25th term of the arithmetic sequence 6, 18, 30, 42, ...
294
First term a = 6 and common difference d = 12. Using a + (n − 1)d gives 6 + 24 × 12 = 294.
8. Find the 23th term of the arithmetic sequence 8, 13, 18, 23, ...
118
First term a = 8 and common difference d = 5. Using a + (n − 1)d gives 8 + 22 × 5 = 118.
9. Find the 24th term of the arithmetic sequence 14, 25, 36, 47, ...
267
First term a = 14 and common difference d = 11. Using a + (n − 1)d gives 14 + 23 × 11 = 267.
10. Find the 19th term of the arithmetic sequence 22, 33, 44, 55, ...
220
First term a = 22 and common difference d = 11. Using a + (n − 1)d gives 22 + 18 × 11 = 220.
11. Find the 18th term of the arithmetic sequence 2, 9, 16, 23, ...
121
First term a = 2 and common difference d = 7. Using a + (n − 1)d gives 2 + 17 × 7 = 121.
12. Find the 19th term of the arithmetic sequence 9, 15, 21, 27, ...
117
First term a = 9 and common difference d = 6. Using a + (n − 1)d gives 9 + 18 × 6 = 117.

12 questions · Seed 49 · Age guidance, not curriculum certification