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 25th term of the arithmetic sequence 16, 24, 32, 40, ...
2. Find the 21th term of the arithmetic sequence 2, 13, 24, 35, ...
3. Find the 8th term of the arithmetic sequence 4, 12, 20, 28, ...
4. Find the 10th term of the arithmetic sequence 7, 12, 17, 22, ...
5. Find the 13th term of the arithmetic sequence 25, 31, 37, 43, ...
6. Find the 22th term of the arithmetic sequence 18, 22, 26, 30, ...
7. Find the 23th term of the arithmetic sequence 5, 16, 27, 38, ...
8. Find the 8th term of the arithmetic sequence 10, 17, 24, 31, ...
9. Find the 20th term of the arithmetic sequence 21, 31, 41, 51, ...
10. Find the 23th term of the arithmetic sequence 25, 28, 31, 34, ...
11. Find the 10th term of the arithmetic sequence 5, 8, 11, 14, ...
12. Find the 17th term of the arithmetic sequence 14, 17, 20, 23, ...

12 questions · Seed 104737 · 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 25th term of the arithmetic sequence 16, 24, 32, 40, ...
208
First term a = 16 and common difference d = 8. Using a + (n − 1)d gives 16 + 24 × 8 = 208.
2. Find the 21th term of the arithmetic sequence 2, 13, 24, 35, ...
222
First term a = 2 and common difference d = 11. Using a + (n − 1)d gives 2 + 20 × 11 = 222.
3. Find the 8th term of the arithmetic sequence 4, 12, 20, 28, ...
60
First term a = 4 and common difference d = 8. Using a + (n − 1)d gives 4 + 7 × 8 = 60.
4. Find the 10th term of the arithmetic sequence 7, 12, 17, 22, ...
52
First term a = 7 and common difference d = 5. Using a + (n − 1)d gives 7 + 9 × 5 = 52.
5. Find the 13th term of the arithmetic sequence 25, 31, 37, 43, ...
97
First term a = 25 and common difference d = 6. Using a + (n − 1)d gives 25 + 12 × 6 = 97.
6. Find the 22th term of the arithmetic sequence 18, 22, 26, 30, ...
102
First term a = 18 and common difference d = 4. Using a + (n − 1)d gives 18 + 21 × 4 = 102.
7. Find the 23th term of the arithmetic sequence 5, 16, 27, 38, ...
247
First term a = 5 and common difference d = 11. Using a + (n − 1)d gives 5 + 22 × 11 = 247.
8. 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.
9. Find the 20th term of the arithmetic sequence 21, 31, 41, 51, ...
211
First term a = 21 and common difference d = 10. Using a + (n − 1)d gives 21 + 19 × 10 = 211.
10. Find the 23th term of the arithmetic sequence 25, 28, 31, 34, ...
91
First term a = 25 and common difference d = 3. Using a + (n − 1)d gives 25 + 22 × 3 = 91.
11. Find the 10th term of the arithmetic sequence 5, 8, 11, 14, ...
32
First term a = 5 and common difference d = 3. Using a + (n − 1)d gives 5 + 9 × 3 = 32.
12. Find the 17th term of the arithmetic sequence 14, 17, 20, 23, ...
62
First term a = 14 and common difference d = 3. Using a + (n − 1)d gives 14 + 16 × 3 = 62.

12 questions · Seed 104737 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Linear nth-term sequences

Take your time. Show your thinking.

1. Find the 25th term of the arithmetic sequence 16, 24, 32, 40, ...
2. Find the 21th term of the arithmetic sequence 2, 13, 24, 35, ...
3. Find the 8th term of the arithmetic sequence 4, 12, 20, 28, ...
4. Find the 10th term of the arithmetic sequence 7, 12, 17, 22, ...
5. Find the 13th term of the arithmetic sequence 25, 31, 37, 43, ...
6. Find the 22th term of the arithmetic sequence 18, 22, 26, 30, ...
7. Find the 23th term of the arithmetic sequence 5, 16, 27, 38, ...
8. Find the 8th term of the arithmetic sequence 10, 17, 24, 31, ...
9. Find the 20th term of the arithmetic sequence 21, 31, 41, 51, ...
10. Find the 23th term of the arithmetic sequence 25, 28, 31, 34, ...
11. Find the 10th term of the arithmetic sequence 5, 8, 11, 14, ...
12. Find the 17th term of the arithmetic sequence 14, 17, 20, 23, ...

12 questions · Seed 104737 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Linear nth-term sequences

Answers and reasoning. Review before teaching.

1. Find the 25th term of the arithmetic sequence 16, 24, 32, 40, ...
208
First term a = 16 and common difference d = 8. Using a + (n − 1)d gives 16 + 24 × 8 = 208.
2. Find the 21th term of the arithmetic sequence 2, 13, 24, 35, ...
222
First term a = 2 and common difference d = 11. Using a + (n − 1)d gives 2 + 20 × 11 = 222.
3. Find the 8th term of the arithmetic sequence 4, 12, 20, 28, ...
60
First term a = 4 and common difference d = 8. Using a + (n − 1)d gives 4 + 7 × 8 = 60.
4. Find the 10th term of the arithmetic sequence 7, 12, 17, 22, ...
52
First term a = 7 and common difference d = 5. Using a + (n − 1)d gives 7 + 9 × 5 = 52.
5. Find the 13th term of the arithmetic sequence 25, 31, 37, 43, ...
97
First term a = 25 and common difference d = 6. Using a + (n − 1)d gives 25 + 12 × 6 = 97.
6. Find the 22th term of the arithmetic sequence 18, 22, 26, 30, ...
102
First term a = 18 and common difference d = 4. Using a + (n − 1)d gives 18 + 21 × 4 = 102.
7. Find the 23th term of the arithmetic sequence 5, 16, 27, 38, ...
247
First term a = 5 and common difference d = 11. Using a + (n − 1)d gives 5 + 22 × 11 = 247.
8. 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.
9. Find the 20th term of the arithmetic sequence 21, 31, 41, 51, ...
211
First term a = 21 and common difference d = 10. Using a + (n − 1)d gives 21 + 19 × 10 = 211.
10. Find the 23th term of the arithmetic sequence 25, 28, 31, 34, ...
91
First term a = 25 and common difference d = 3. Using a + (n − 1)d gives 25 + 22 × 3 = 91.
11. Find the 10th term of the arithmetic sequence 5, 8, 11, 14, ...
32
First term a = 5 and common difference d = 3. Using a + (n − 1)d gives 5 + 9 × 3 = 32.
12. Find the 17th term of the arithmetic sequence 14, 17, 20, 23, ...
62
First term a = 14 and common difference d = 3. Using a + (n − 1)d gives 14 + 16 × 3 = 62.

12 questions · Seed 104737 · Age guidance, not curriculum certification