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 16, 21, 26, 31, ...
2. Find the 11th term of the arithmetic sequence 10, 13, 16, 19, ...
3. Find the 9th term of the arithmetic sequence 15, 21, 27, 33, ...
4. Find the 25th term of the arithmetic sequence 19, 26, 33, 40, ...
5. Find the 19th term of the arithmetic sequence 4, 10, 16, 22, ...
6. Find the 21th term of the arithmetic sequence 4, 6, 8, 10, ...
7. Find the 18th term of the arithmetic sequence 20, 23, 26, 29, ...
8. Find the 18th term of the arithmetic sequence 24, 28, 32, 36, ...
9. Find the 8th term of the arithmetic sequence 24, 31, 38, 45, ...
10. Find the 9th term of the arithmetic sequence 19, 28, 37, 46, ...
11. Find the 19th term of the arithmetic sequence 11, 18, 25, 32, ...
12. Find the 13th term of the arithmetic sequence 16, 20, 24, 28, ...

12 questions · Seed 55 · 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 16, 21, 26, 31, ...
71
First term a = 16 and common difference d = 5. Using a + (n − 1)d gives 16 + 11 × 5 = 71.
2. Find the 11th term of the arithmetic sequence 10, 13, 16, 19, ...
40
First term a = 10 and common difference d = 3. Using a + (n − 1)d gives 10 + 10 × 3 = 40.
3. Find the 9th term of the arithmetic sequence 15, 21, 27, 33, ...
63
First term a = 15 and common difference d = 6. Using a + (n − 1)d gives 15 + 8 × 6 = 63.
4. Find the 25th term of the arithmetic sequence 19, 26, 33, 40, ...
187
First term a = 19 and common difference d = 7. Using a + (n − 1)d gives 19 + 24 × 7 = 187.
5. Find the 19th term of the arithmetic sequence 4, 10, 16, 22, ...
112
First term a = 4 and common difference d = 6. Using a + (n − 1)d gives 4 + 18 × 6 = 112.
6. Find the 21th term of the arithmetic sequence 4, 6, 8, 10, ...
44
First term a = 4 and common difference d = 2. Using a + (n − 1)d gives 4 + 20 × 2 = 44.
7. Find the 18th term of the arithmetic sequence 20, 23, 26, 29, ...
71
First term a = 20 and common difference d = 3. Using a + (n − 1)d gives 20 + 17 × 3 = 71.
8. Find the 18th term of the arithmetic sequence 24, 28, 32, 36, ...
92
First term a = 24 and common difference d = 4. Using a + (n − 1)d gives 24 + 17 × 4 = 92.
9. Find the 8th term of the arithmetic sequence 24, 31, 38, 45, ...
73
First term a = 24 and common difference d = 7. Using a + (n − 1)d gives 24 + 7 × 7 = 73.
10. Find the 9th term of the arithmetic sequence 19, 28, 37, 46, ...
91
First term a = 19 and common difference d = 9. Using a + (n − 1)d gives 19 + 8 × 9 = 91.
11. Find the 19th term of the arithmetic sequence 11, 18, 25, 32, ...
137
First term a = 11 and common difference d = 7. Using a + (n − 1)d gives 11 + 18 × 7 = 137.
12. Find the 13th term of the arithmetic sequence 16, 20, 24, 28, ...
64
First term a = 16 and common difference d = 4. Using a + (n − 1)d gives 16 + 12 × 4 = 64.

12 questions · Seed 55 · 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 16, 21, 26, 31, ...
2. Find the 11th term of the arithmetic sequence 10, 13, 16, 19, ...
3. Find the 9th term of the arithmetic sequence 15, 21, 27, 33, ...
4. Find the 25th term of the arithmetic sequence 19, 26, 33, 40, ...
5. Find the 19th term of the arithmetic sequence 4, 10, 16, 22, ...
6. Find the 21th term of the arithmetic sequence 4, 6, 8, 10, ...
7. Find the 18th term of the arithmetic sequence 20, 23, 26, 29, ...
8. Find the 18th term of the arithmetic sequence 24, 28, 32, 36, ...
9. Find the 8th term of the arithmetic sequence 24, 31, 38, 45, ...
10. Find the 9th term of the arithmetic sequence 19, 28, 37, 46, ...
11. Find the 19th term of the arithmetic sequence 11, 18, 25, 32, ...
12. Find the 13th term of the arithmetic sequence 16, 20, 24, 28, ...

12 questions · Seed 55 · 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 16, 21, 26, 31, ...
71
First term a = 16 and common difference d = 5. Using a + (n − 1)d gives 16 + 11 × 5 = 71.
2. Find the 11th term of the arithmetic sequence 10, 13, 16, 19, ...
40
First term a = 10 and common difference d = 3. Using a + (n − 1)d gives 10 + 10 × 3 = 40.
3. Find the 9th term of the arithmetic sequence 15, 21, 27, 33, ...
63
First term a = 15 and common difference d = 6. Using a + (n − 1)d gives 15 + 8 × 6 = 63.
4. Find the 25th term of the arithmetic sequence 19, 26, 33, 40, ...
187
First term a = 19 and common difference d = 7. Using a + (n − 1)d gives 19 + 24 × 7 = 187.
5. Find the 19th term of the arithmetic sequence 4, 10, 16, 22, ...
112
First term a = 4 and common difference d = 6. Using a + (n − 1)d gives 4 + 18 × 6 = 112.
6. Find the 21th term of the arithmetic sequence 4, 6, 8, 10, ...
44
First term a = 4 and common difference d = 2. Using a + (n − 1)d gives 4 + 20 × 2 = 44.
7. Find the 18th term of the arithmetic sequence 20, 23, 26, 29, ...
71
First term a = 20 and common difference d = 3. Using a + (n − 1)d gives 20 + 17 × 3 = 71.
8. Find the 18th term of the arithmetic sequence 24, 28, 32, 36, ...
92
First term a = 24 and common difference d = 4. Using a + (n − 1)d gives 24 + 17 × 4 = 92.
9. Find the 8th term of the arithmetic sequence 24, 31, 38, 45, ...
73
First term a = 24 and common difference d = 7. Using a + (n − 1)d gives 24 + 7 × 7 = 73.
10. Find the 9th term of the arithmetic sequence 19, 28, 37, 46, ...
91
First term a = 19 and common difference d = 9. Using a + (n − 1)d gives 19 + 8 × 9 = 91.
11. Find the 19th term of the arithmetic sequence 11, 18, 25, 32, ...
137
First term a = 11 and common difference d = 7. Using a + (n − 1)d gives 11 + 18 × 7 = 137.
12. Find the 13th term of the arithmetic sequence 16, 20, 24, 28, ...
64
First term a = 16 and common difference d = 4. Using a + (n − 1)d gives 16 + 12 × 4 = 64.

12 questions · Seed 55 · Age guidance, not curriculum certification