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 15th term of the arithmetic sequence 7, 19, 31, 43, ...
2. Find the 9th term of the arithmetic sequence 3, 11, 19, 27, ...
3. Find the 14th term of the arithmetic sequence 5, 15, 25, 35, ...
4. Find the 24th term of the arithmetic sequence 23, 32, 41, 50, ...
5. Find the 18th term of the arithmetic sequence 22, 31, 40, 49, ...
6. Find the 17th term of the arithmetic sequence 6, 15, 24, 33, ...
7. Find the 12th term of the arithmetic sequence 5, 12, 19, 26, ...
8. Find the 10th term of the arithmetic sequence 17, 26, 35, 44, ...
9. Find the 13th term of the arithmetic sequence 19, 22, 25, 28, ...
10. Find the 8th term of the arithmetic sequence 10, 17, 24, 31, ...
11. Find the 21th term of the arithmetic sequence 15, 19, 23, 27, ...
12. Find the 8th term of the arithmetic sequence 10, 20, 30, 40, ...

12 questions · Seed 46 · 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 15th term of the arithmetic sequence 7, 19, 31, 43, ...
175
First term a = 7 and common difference d = 12. Using a + (n − 1)d gives 7 + 14 × 12 = 175.
2. Find the 9th term of the arithmetic sequence 3, 11, 19, 27, ...
67
First term a = 3 and common difference d = 8. Using a + (n − 1)d gives 3 + 8 × 8 = 67.
3. Find the 14th term of the arithmetic sequence 5, 15, 25, 35, ...
135
First term a = 5 and common difference d = 10. Using a + (n − 1)d gives 5 + 13 × 10 = 135.
4. Find the 24th term of the arithmetic sequence 23, 32, 41, 50, ...
230
First term a = 23 and common difference d = 9. Using a + (n − 1)d gives 23 + 23 × 9 = 230.
5. Find the 18th term of the arithmetic sequence 22, 31, 40, 49, ...
175
First term a = 22 and common difference d = 9. Using a + (n − 1)d gives 22 + 17 × 9 = 175.
6. Find the 17th term of the arithmetic sequence 6, 15, 24, 33, ...
150
First term a = 6 and common difference d = 9. Using a + (n − 1)d gives 6 + 16 × 9 = 150.
7. Find the 12th term of the arithmetic sequence 5, 12, 19, 26, ...
82
First term a = 5 and common difference d = 7. Using a + (n − 1)d gives 5 + 11 × 7 = 82.
8. Find the 10th term of the arithmetic sequence 17, 26, 35, 44, ...
98
First term a = 17 and common difference d = 9. Using a + (n − 1)d gives 17 + 9 × 9 = 98.
9. Find the 13th term of the arithmetic sequence 19, 22, 25, 28, ...
55
First term a = 19 and common difference d = 3. Using a + (n − 1)d gives 19 + 12 × 3 = 55.
10. Find the 8th term of the arithmetic sequence 10, 17, 24, 31, ...
59
First term a = 10 and common difference d = 7. Using a + (n − 1)d gives 10 + 7 × 7 = 59.
11. Find the 21th term of the arithmetic sequence 15, 19, 23, 27, ...
95
First term a = 15 and common difference d = 4. Using a + (n − 1)d gives 15 + 20 × 4 = 95.
12. Find the 8th term of the arithmetic sequence 10, 20, 30, 40, ...
80
First term a = 10 and common difference d = 10. Using a + (n − 1)d gives 10 + 7 × 10 = 80.

12 questions · Seed 46 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Linear nth-term sequences

Take your time. Show your thinking.

1. Find the 15th term of the arithmetic sequence 7, 19, 31, 43, ...
2. Find the 9th term of the arithmetic sequence 3, 11, 19, 27, ...
3. Find the 14th term of the arithmetic sequence 5, 15, 25, 35, ...
4. Find the 24th term of the arithmetic sequence 23, 32, 41, 50, ...
5. Find the 18th term of the arithmetic sequence 22, 31, 40, 49, ...
6. Find the 17th term of the arithmetic sequence 6, 15, 24, 33, ...
7. Find the 12th term of the arithmetic sequence 5, 12, 19, 26, ...
8. Find the 10th term of the arithmetic sequence 17, 26, 35, 44, ...
9. Find the 13th term of the arithmetic sequence 19, 22, 25, 28, ...
10. Find the 8th term of the arithmetic sequence 10, 17, 24, 31, ...
11. Find the 21th term of the arithmetic sequence 15, 19, 23, 27, ...
12. Find the 8th term of the arithmetic sequence 10, 20, 30, 40, ...

12 questions · Seed 46 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Linear nth-term sequences

Answers and reasoning. Review before teaching.

1. Find the 15th term of the arithmetic sequence 7, 19, 31, 43, ...
175
First term a = 7 and common difference d = 12. Using a + (n − 1)d gives 7 + 14 × 12 = 175.
2. Find the 9th term of the arithmetic sequence 3, 11, 19, 27, ...
67
First term a = 3 and common difference d = 8. Using a + (n − 1)d gives 3 + 8 × 8 = 67.
3. Find the 14th term of the arithmetic sequence 5, 15, 25, 35, ...
135
First term a = 5 and common difference d = 10. Using a + (n − 1)d gives 5 + 13 × 10 = 135.
4. Find the 24th term of the arithmetic sequence 23, 32, 41, 50, ...
230
First term a = 23 and common difference d = 9. Using a + (n − 1)d gives 23 + 23 × 9 = 230.
5. Find the 18th term of the arithmetic sequence 22, 31, 40, 49, ...
175
First term a = 22 and common difference d = 9. Using a + (n − 1)d gives 22 + 17 × 9 = 175.
6. Find the 17th term of the arithmetic sequence 6, 15, 24, 33, ...
150
First term a = 6 and common difference d = 9. Using a + (n − 1)d gives 6 + 16 × 9 = 150.
7. Find the 12th term of the arithmetic sequence 5, 12, 19, 26, ...
82
First term a = 5 and common difference d = 7. Using a + (n − 1)d gives 5 + 11 × 7 = 82.
8. Find the 10th term of the arithmetic sequence 17, 26, 35, 44, ...
98
First term a = 17 and common difference d = 9. Using a + (n − 1)d gives 17 + 9 × 9 = 98.
9. Find the 13th term of the arithmetic sequence 19, 22, 25, 28, ...
55
First term a = 19 and common difference d = 3. Using a + (n − 1)d gives 19 + 12 × 3 = 55.
10. Find the 8th term of the arithmetic sequence 10, 17, 24, 31, ...
59
First term a = 10 and common difference d = 7. Using a + (n − 1)d gives 10 + 7 × 7 = 59.
11. Find the 21th term of the arithmetic sequence 15, 19, 23, 27, ...
95
First term a = 15 and common difference d = 4. Using a + (n − 1)d gives 15 + 20 × 4 = 95.
12. Find the 8th term of the arithmetic sequence 10, 20, 30, 40, ...
80
First term a = 10 and common difference d = 10. Using a + (n − 1)d gives 10 + 7 × 10 = 80.

12 questions · Seed 46 · Age guidance, not curriculum certification