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 11th term of the arithmetic sequence 10, 17, 24, 31, ...
2. Find the 11th term of the arithmetic sequence 19, 21, 23, 25, ...
3. Find the 22th term of the arithmetic sequence 12, 21, 30, 39, ...
4. Find the 20th term of the arithmetic sequence 6, 16, 26, 36, ...
5. Find the 16th term of the arithmetic sequence 12, 16, 20, 24, ...
6. Find the 25th term of the arithmetic sequence 24, 27, 30, 33, ...
7. Find the 10th term of the arithmetic sequence 25, 27, 29, 31, ...
8. Find the 11th term of the arithmetic sequence 13, 16, 19, 22, ...
9. Find the 14th term of the arithmetic sequence 2, 12, 22, 32, ...
10. Find the 12th term of the arithmetic sequence 13, 18, 23, 28, ...
11. Find the 19th term of the arithmetic sequence 22, 24, 26, 28, ...
12. Find the 21th term of the arithmetic sequence 2, 4, 6, 8, ...

12 questions · Seed 104742 · Age guidance, not curriculum certification

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Worksheet StudioAnswer key · Ages 13-15

Linear nth-term sequences

Answers and reasoning. Review before teaching.

1. Find the 11th term of the arithmetic sequence 10, 17, 24, 31, ...
80
First term a = 10 and common difference d = 7. Using a + (n − 1)d gives 10 + 10 × 7 = 80.
2. Find the 11th term of the arithmetic sequence 19, 21, 23, 25, ...
39
First term a = 19 and common difference d = 2. Using a + (n − 1)d gives 19 + 10 × 2 = 39.
3. Find the 22th term of the arithmetic sequence 12, 21, 30, 39, ...
201
First term a = 12 and common difference d = 9. Using a + (n − 1)d gives 12 + 21 × 9 = 201.
4. Find the 20th term of the arithmetic sequence 6, 16, 26, 36, ...
196
First term a = 6 and common difference d = 10. Using a + (n − 1)d gives 6 + 19 × 10 = 196.
5. Find the 16th term of the arithmetic sequence 12, 16, 20, 24, ...
72
First term a = 12 and common difference d = 4. Using a + (n − 1)d gives 12 + 15 × 4 = 72.
6. Find the 25th term of the arithmetic sequence 24, 27, 30, 33, ...
96
First term a = 24 and common difference d = 3. Using a + (n − 1)d gives 24 + 24 × 3 = 96.
7. Find the 10th term of the arithmetic sequence 25, 27, 29, 31, ...
43
First term a = 25 and common difference d = 2. Using a + (n − 1)d gives 25 + 9 × 2 = 43.
8. Find the 11th term of the arithmetic sequence 13, 16, 19, 22, ...
43
First term a = 13 and common difference d = 3. Using a + (n − 1)d gives 13 + 10 × 3 = 43.
9. Find the 14th term of the arithmetic sequence 2, 12, 22, 32, ...
132
First term a = 2 and common difference d = 10. Using a + (n − 1)d gives 2 + 13 × 10 = 132.
10. Find the 12th term of the arithmetic sequence 13, 18, 23, 28, ...
68
First term a = 13 and common difference d = 5. Using a + (n − 1)d gives 13 + 11 × 5 = 68.
11. Find the 19th term of the arithmetic sequence 22, 24, 26, 28, ...
58
First term a = 22 and common difference d = 2. Using a + (n − 1)d gives 22 + 18 × 2 = 58.
12. Find the 21th term of the arithmetic sequence 2, 4, 6, 8, ...
42
First term a = 2 and common difference d = 2. Using a + (n − 1)d gives 2 + 20 × 2 = 42.

12 questions · Seed 104742 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Linear nth-term sequences

Take your time. Show your thinking.

1. Find the 11th term of the arithmetic sequence 10, 17, 24, 31, ...
2. Find the 11th term of the arithmetic sequence 19, 21, 23, 25, ...
3. Find the 22th term of the arithmetic sequence 12, 21, 30, 39, ...
4. Find the 20th term of the arithmetic sequence 6, 16, 26, 36, ...
5. Find the 16th term of the arithmetic sequence 12, 16, 20, 24, ...
6. Find the 25th term of the arithmetic sequence 24, 27, 30, 33, ...
7. Find the 10th term of the arithmetic sequence 25, 27, 29, 31, ...
8. Find the 11th term of the arithmetic sequence 13, 16, 19, 22, ...
9. Find the 14th term of the arithmetic sequence 2, 12, 22, 32, ...
10. Find the 12th term of the arithmetic sequence 13, 18, 23, 28, ...
11. Find the 19th term of the arithmetic sequence 22, 24, 26, 28, ...
12. Find the 21th term of the arithmetic sequence 2, 4, 6, 8, ...

12 questions · Seed 104742 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Linear nth-term sequences

Answers and reasoning. Review before teaching.

1. Find the 11th term of the arithmetic sequence 10, 17, 24, 31, ...
80
First term a = 10 and common difference d = 7. Using a + (n − 1)d gives 10 + 10 × 7 = 80.
2. Find the 11th term of the arithmetic sequence 19, 21, 23, 25, ...
39
First term a = 19 and common difference d = 2. Using a + (n − 1)d gives 19 + 10 × 2 = 39.
3. Find the 22th term of the arithmetic sequence 12, 21, 30, 39, ...
201
First term a = 12 and common difference d = 9. Using a + (n − 1)d gives 12 + 21 × 9 = 201.
4. Find the 20th term of the arithmetic sequence 6, 16, 26, 36, ...
196
First term a = 6 and common difference d = 10. Using a + (n − 1)d gives 6 + 19 × 10 = 196.
5. Find the 16th term of the arithmetic sequence 12, 16, 20, 24, ...
72
First term a = 12 and common difference d = 4. Using a + (n − 1)d gives 12 + 15 × 4 = 72.
6. Find the 25th term of the arithmetic sequence 24, 27, 30, 33, ...
96
First term a = 24 and common difference d = 3. Using a + (n − 1)d gives 24 + 24 × 3 = 96.
7. Find the 10th term of the arithmetic sequence 25, 27, 29, 31, ...
43
First term a = 25 and common difference d = 2. Using a + (n − 1)d gives 25 + 9 × 2 = 43.
8. Find the 11th term of the arithmetic sequence 13, 16, 19, 22, ...
43
First term a = 13 and common difference d = 3. Using a + (n − 1)d gives 13 + 10 × 3 = 43.
9. Find the 14th term of the arithmetic sequence 2, 12, 22, 32, ...
132
First term a = 2 and common difference d = 10. Using a + (n − 1)d gives 2 + 13 × 10 = 132.
10. Find the 12th term of the arithmetic sequence 13, 18, 23, 28, ...
68
First term a = 13 and common difference d = 5. Using a + (n − 1)d gives 13 + 11 × 5 = 68.
11. Find the 19th term of the arithmetic sequence 22, 24, 26, 28, ...
58
First term a = 22 and common difference d = 2. Using a + (n − 1)d gives 22 + 18 × 2 = 58.
12. Find the 21th term of the arithmetic sequence 2, 4, 6, 8, ...
42
First term a = 2 and common difference d = 2. Using a + (n − 1)d gives 2 + 20 × 2 = 42.

12 questions · Seed 104742 · Age guidance, not curriculum certification