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 8th term of the arithmetic sequence 5, 10, 15, 20, ...
2. Find the 10th term of the arithmetic sequence 4, 8, 12, 16, ...
3. Find the 11th term of the arithmetic sequence 14, 23, 32, 41, ...
4. Find the 24th term of the arithmetic sequence 13, 16, 19, 22, ...
5. Find the 22th term of the arithmetic sequence 3, 7, 11, 15, ...
6. Find the 23th term of the arithmetic sequence 8, 13, 18, 23, ...
7. Find the 9th term of the arithmetic sequence 11, 15, 19, 23, ...
8. Find the 23th term of the arithmetic sequence 14, 18, 22, 26, ...
9. Find the 13th term of the arithmetic sequence 22, 27, 32, 37, ...
10. Find the 12th term of the arithmetic sequence 19, 24, 29, 34, ...
11. Find the 19th term of the arithmetic sequence 13, 19, 25, 31, ...
12. Find the 9th term of the arithmetic sequence 12, 18, 24, 30, ...

12 questions · Seed 104744 · 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 8th term of the arithmetic sequence 5, 10, 15, 20, ...
40
First term a = 5 and common difference d = 5. Using a + (n − 1)d gives 5 + 7 × 5 = 40.
2. Find the 10th term of the arithmetic sequence 4, 8, 12, 16, ...
40
First term a = 4 and common difference d = 4. Using a + (n − 1)d gives 4 + 9 × 4 = 40.
3. Find the 11th term of the arithmetic sequence 14, 23, 32, 41, ...
104
First term a = 14 and common difference d = 9. Using a + (n − 1)d gives 14 + 10 × 9 = 104.
4. Find the 24th term of the arithmetic sequence 13, 16, 19, 22, ...
82
First term a = 13 and common difference d = 3. Using a + (n − 1)d gives 13 + 23 × 3 = 82.
5. Find the 22th term of the arithmetic sequence 3, 7, 11, 15, ...
87
First term a = 3 and common difference d = 4. Using a + (n − 1)d gives 3 + 21 × 4 = 87.
6. 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.
7. Find the 9th term of the arithmetic sequence 11, 15, 19, 23, ...
43
First term a = 11 and common difference d = 4. Using a + (n − 1)d gives 11 + 8 × 4 = 43.
8. Find the 23th term of the arithmetic sequence 14, 18, 22, 26, ...
102
First term a = 14 and common difference d = 4. Using a + (n − 1)d gives 14 + 22 × 4 = 102.
9. Find the 13th term of the arithmetic sequence 22, 27, 32, 37, ...
82
First term a = 22 and common difference d = 5. Using a + (n − 1)d gives 22 + 12 × 5 = 82.
10. Find the 12th term of the arithmetic sequence 19, 24, 29, 34, ...
74
First term a = 19 and common difference d = 5. Using a + (n − 1)d gives 19 + 11 × 5 = 74.
11. Find the 19th term of the arithmetic sequence 13, 19, 25, 31, ...
121
First term a = 13 and common difference d = 6. Using a + (n − 1)d gives 13 + 18 × 6 = 121.
12. Find the 9th term of the arithmetic sequence 12, 18, 24, 30, ...
60
First term a = 12 and common difference d = 6. Using a + (n − 1)d gives 12 + 8 × 6 = 60.

12 questions · Seed 104744 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Linear nth-term sequences

Take your time. Show your thinking.

1. Find the 8th term of the arithmetic sequence 5, 10, 15, 20, ...
2. Find the 10th term of the arithmetic sequence 4, 8, 12, 16, ...
3. Find the 11th term of the arithmetic sequence 14, 23, 32, 41, ...
4. Find the 24th term of the arithmetic sequence 13, 16, 19, 22, ...
5. Find the 22th term of the arithmetic sequence 3, 7, 11, 15, ...
6. Find the 23th term of the arithmetic sequence 8, 13, 18, 23, ...
7. Find the 9th term of the arithmetic sequence 11, 15, 19, 23, ...
8. Find the 23th term of the arithmetic sequence 14, 18, 22, 26, ...
9. Find the 13th term of the arithmetic sequence 22, 27, 32, 37, ...
10. Find the 12th term of the arithmetic sequence 19, 24, 29, 34, ...
11. Find the 19th term of the arithmetic sequence 13, 19, 25, 31, ...
12. Find the 9th term of the arithmetic sequence 12, 18, 24, 30, ...

12 questions · Seed 104744 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Linear nth-term sequences

Answers and reasoning. Review before teaching.

1. Find the 8th term of the arithmetic sequence 5, 10, 15, 20, ...
40
First term a = 5 and common difference d = 5. Using a + (n − 1)d gives 5 + 7 × 5 = 40.
2. Find the 10th term of the arithmetic sequence 4, 8, 12, 16, ...
40
First term a = 4 and common difference d = 4. Using a + (n − 1)d gives 4 + 9 × 4 = 40.
3. Find the 11th term of the arithmetic sequence 14, 23, 32, 41, ...
104
First term a = 14 and common difference d = 9. Using a + (n − 1)d gives 14 + 10 × 9 = 104.
4. Find the 24th term of the arithmetic sequence 13, 16, 19, 22, ...
82
First term a = 13 and common difference d = 3. Using a + (n − 1)d gives 13 + 23 × 3 = 82.
5. Find the 22th term of the arithmetic sequence 3, 7, 11, 15, ...
87
First term a = 3 and common difference d = 4. Using a + (n − 1)d gives 3 + 21 × 4 = 87.
6. 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.
7. Find the 9th term of the arithmetic sequence 11, 15, 19, 23, ...
43
First term a = 11 and common difference d = 4. Using a + (n − 1)d gives 11 + 8 × 4 = 43.
8. Find the 23th term of the arithmetic sequence 14, 18, 22, 26, ...
102
First term a = 14 and common difference d = 4. Using a + (n − 1)d gives 14 + 22 × 4 = 102.
9. Find the 13th term of the arithmetic sequence 22, 27, 32, 37, ...
82
First term a = 22 and common difference d = 5. Using a + (n − 1)d gives 22 + 12 × 5 = 82.
10. Find the 12th term of the arithmetic sequence 19, 24, 29, 34, ...
74
First term a = 19 and common difference d = 5. Using a + (n − 1)d gives 19 + 11 × 5 = 74.
11. Find the 19th term of the arithmetic sequence 13, 19, 25, 31, ...
121
First term a = 13 and common difference d = 6. Using a + (n − 1)d gives 13 + 18 × 6 = 121.
12. Find the 9th term of the arithmetic sequence 12, 18, 24, 30, ...
60
First term a = 12 and common difference d = 6. Using a + (n − 1)d gives 12 + 8 × 6 = 60.

12 questions · Seed 104744 · Age guidance, not curriculum certification