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 20th term of the arithmetic sequence 19, 31, 43, 55, ...
2. Find the 13th term of the arithmetic sequence 6, 17, 28, 39, ...
3. Find the 13th term of the arithmetic sequence 14, 23, 32, 41, ...
4. Find the 12th term of the arithmetic sequence 13, 16, 19, 22, ...
5. Find the 17th term of the arithmetic sequence 16, 21, 26, 31, ...
6. Find the 14th term of the arithmetic sequence 17, 26, 35, 44, ...
7. Find the 15th term of the arithmetic sequence 20, 28, 36, 44, ...
8. Find the 12th term of the arithmetic sequence 6, 17, 28, 39, ...
9. Find the 11th term of the arithmetic sequence 7, 13, 19, 25, ...
10. Find the 10th term of the arithmetic sequence 21, 27, 33, 39, ...
11. Find the 11th term of the arithmetic sequence 18, 29, 40, 51, ...
12. Find the 20th term of the arithmetic sequence 10, 21, 32, 43, ...

12 questions · Seed 104735 · 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 20th term of the arithmetic sequence 19, 31, 43, 55, ...
247
First term a = 19 and common difference d = 12. Using a + (n − 1)d gives 19 + 19 × 12 = 247.
2. Find the 13th term of the arithmetic sequence 6, 17, 28, 39, ...
138
First term a = 6 and common difference d = 11. Using a + (n − 1)d gives 6 + 12 × 11 = 138.
3. Find the 13th term of the arithmetic sequence 14, 23, 32, 41, ...
122
First term a = 14 and common difference d = 9. Using a + (n − 1)d gives 14 + 12 × 9 = 122.
4. Find the 12th term of the arithmetic sequence 13, 16, 19, 22, ...
46
First term a = 13 and common difference d = 3. Using a + (n − 1)d gives 13 + 11 × 3 = 46.
5. Find the 17th term of the arithmetic sequence 16, 21, 26, 31, ...
96
First term a = 16 and common difference d = 5. Using a + (n − 1)d gives 16 + 16 × 5 = 96.
6. Find the 14th term of the arithmetic sequence 17, 26, 35, 44, ...
134
First term a = 17 and common difference d = 9. Using a + (n − 1)d gives 17 + 13 × 9 = 134.
7. Find the 15th term of the arithmetic sequence 20, 28, 36, 44, ...
132
First term a = 20 and common difference d = 8. Using a + (n − 1)d gives 20 + 14 × 8 = 132.
8. Find the 12th term of the arithmetic sequence 6, 17, 28, 39, ...
127
First term a = 6 and common difference d = 11. Using a + (n − 1)d gives 6 + 11 × 11 = 127.
9. Find the 11th term of the arithmetic sequence 7, 13, 19, 25, ...
67
First term a = 7 and common difference d = 6. Using a + (n − 1)d gives 7 + 10 × 6 = 67.
10. Find the 10th term of the arithmetic sequence 21, 27, 33, 39, ...
75
First term a = 21 and common difference d = 6. Using a + (n − 1)d gives 21 + 9 × 6 = 75.
11. Find the 11th term of the arithmetic sequence 18, 29, 40, 51, ...
128
First term a = 18 and common difference d = 11. Using a + (n − 1)d gives 18 + 10 × 11 = 128.
12. Find the 20th term of the arithmetic sequence 10, 21, 32, 43, ...
219
First term a = 10 and common difference d = 11. Using a + (n − 1)d gives 10 + 19 × 11 = 219.

12 questions · Seed 104735 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Linear nth-term sequences

Take your time. Show your thinking.

1. Find the 20th term of the arithmetic sequence 19, 31, 43, 55, ...
2. Find the 13th term of the arithmetic sequence 6, 17, 28, 39, ...
3. Find the 13th term of the arithmetic sequence 14, 23, 32, 41, ...
4. Find the 12th term of the arithmetic sequence 13, 16, 19, 22, ...
5. Find the 17th term of the arithmetic sequence 16, 21, 26, 31, ...
6. Find the 14th term of the arithmetic sequence 17, 26, 35, 44, ...
7. Find the 15th term of the arithmetic sequence 20, 28, 36, 44, ...
8. Find the 12th term of the arithmetic sequence 6, 17, 28, 39, ...
9. Find the 11th term of the arithmetic sequence 7, 13, 19, 25, ...
10. Find the 10th term of the arithmetic sequence 21, 27, 33, 39, ...
11. Find the 11th term of the arithmetic sequence 18, 29, 40, 51, ...
12. Find the 20th term of the arithmetic sequence 10, 21, 32, 43, ...

12 questions · Seed 104735 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Linear nth-term sequences

Answers and reasoning. Review before teaching.

1. Find the 20th term of the arithmetic sequence 19, 31, 43, 55, ...
247
First term a = 19 and common difference d = 12. Using a + (n − 1)d gives 19 + 19 × 12 = 247.
2. Find the 13th term of the arithmetic sequence 6, 17, 28, 39, ...
138
First term a = 6 and common difference d = 11. Using a + (n − 1)d gives 6 + 12 × 11 = 138.
3. Find the 13th term of the arithmetic sequence 14, 23, 32, 41, ...
122
First term a = 14 and common difference d = 9. Using a + (n − 1)d gives 14 + 12 × 9 = 122.
4. Find the 12th term of the arithmetic sequence 13, 16, 19, 22, ...
46
First term a = 13 and common difference d = 3. Using a + (n − 1)d gives 13 + 11 × 3 = 46.
5. Find the 17th term of the arithmetic sequence 16, 21, 26, 31, ...
96
First term a = 16 and common difference d = 5. Using a + (n − 1)d gives 16 + 16 × 5 = 96.
6. Find the 14th term of the arithmetic sequence 17, 26, 35, 44, ...
134
First term a = 17 and common difference d = 9. Using a + (n − 1)d gives 17 + 13 × 9 = 134.
7. Find the 15th term of the arithmetic sequence 20, 28, 36, 44, ...
132
First term a = 20 and common difference d = 8. Using a + (n − 1)d gives 20 + 14 × 8 = 132.
8. Find the 12th term of the arithmetic sequence 6, 17, 28, 39, ...
127
First term a = 6 and common difference d = 11. Using a + (n − 1)d gives 6 + 11 × 11 = 127.
9. Find the 11th term of the arithmetic sequence 7, 13, 19, 25, ...
67
First term a = 7 and common difference d = 6. Using a + (n − 1)d gives 7 + 10 × 6 = 67.
10. Find the 10th term of the arithmetic sequence 21, 27, 33, 39, ...
75
First term a = 21 and common difference d = 6. Using a + (n − 1)d gives 21 + 9 × 6 = 75.
11. Find the 11th term of the arithmetic sequence 18, 29, 40, 51, ...
128
First term a = 18 and common difference d = 11. Using a + (n − 1)d gives 18 + 10 × 11 = 128.
12. Find the 20th term of the arithmetic sequence 10, 21, 32, 43, ...
219
First term a = 10 and common difference d = 11. Using a + (n − 1)d gives 10 + 19 × 11 = 219.

12 questions · Seed 104735 · Age guidance, not curriculum certification