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 23th term of the arithmetic sequence 7, 15, 23, 31, ...
2. Find the 8th term of the arithmetic sequence 13, 16, 19, 22, ...
3. Find the 13th term of the arithmetic sequence 2, 10, 18, 26, ...
4. Find the 17th term of the arithmetic sequence 5, 8, 11, 14, ...
5. Find the 25th term of the arithmetic sequence 2, 5, 8, 11, ...
6. Find the 9th term of the arithmetic sequence 4, 16, 28, 40, ...
7. Find the 11th term of the arithmetic sequence 25, 36, 47, 58, ...
8. Find the 25th term of the arithmetic sequence 20, 28, 36, 44, ...
9. Find the 17th term of the arithmetic sequence 7, 15, 23, 31, ...
10. Find the 14th term of the arithmetic sequence 10, 15, 20, 25, ...
11. Find the 9th term of the arithmetic sequence 10, 17, 24, 31, ...
12. Find the 11th term of the arithmetic sequence 17, 25, 33, 41, ...

12 questions · Seed 104733 · 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 23th term of the arithmetic sequence 7, 15, 23, 31, ...
183
First term a = 7 and common difference d = 8. Using a + (n − 1)d gives 7 + 22 × 8 = 183.
2. Find the 8th term of the arithmetic sequence 13, 16, 19, 22, ...
34
First term a = 13 and common difference d = 3. Using a + (n − 1)d gives 13 + 7 × 3 = 34.
3. Find the 13th term of the arithmetic sequence 2, 10, 18, 26, ...
98
First term a = 2 and common difference d = 8. Using a + (n − 1)d gives 2 + 12 × 8 = 98.
4. Find the 17th term of the arithmetic sequence 5, 8, 11, 14, ...
53
First term a = 5 and common difference d = 3. Using a + (n − 1)d gives 5 + 16 × 3 = 53.
5. Find the 25th term of the arithmetic sequence 2, 5, 8, 11, ...
74
First term a = 2 and common difference d = 3. Using a + (n − 1)d gives 2 + 24 × 3 = 74.
6. Find the 9th term of the arithmetic sequence 4, 16, 28, 40, ...
100
First term a = 4 and common difference d = 12. Using a + (n − 1)d gives 4 + 8 × 12 = 100.
7. Find the 11th term of the arithmetic sequence 25, 36, 47, 58, ...
135
First term a = 25 and common difference d = 11. Using a + (n − 1)d gives 25 + 10 × 11 = 135.
8. Find the 25th term of the arithmetic sequence 20, 28, 36, 44, ...
212
First term a = 20 and common difference d = 8. Using a + (n − 1)d gives 20 + 24 × 8 = 212.
9. Find the 17th term of the arithmetic sequence 7, 15, 23, 31, ...
135
First term a = 7 and common difference d = 8. Using a + (n − 1)d gives 7 + 16 × 8 = 135.
10. Find the 14th term of the arithmetic sequence 10, 15, 20, 25, ...
75
First term a = 10 and common difference d = 5. Using a + (n − 1)d gives 10 + 13 × 5 = 75.
11. Find the 9th term of the arithmetic sequence 10, 17, 24, 31, ...
66
First term a = 10 and common difference d = 7. Using a + (n − 1)d gives 10 + 8 × 7 = 66.
12. Find the 11th term of the arithmetic sequence 17, 25, 33, 41, ...
97
First term a = 17 and common difference d = 8. Using a + (n − 1)d gives 17 + 10 × 8 = 97.

12 questions · Seed 104733 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Linear nth-term sequences

Take your time. Show your thinking.

1. Find the 23th term of the arithmetic sequence 7, 15, 23, 31, ...
2. Find the 8th term of the arithmetic sequence 13, 16, 19, 22, ...
3. Find the 13th term of the arithmetic sequence 2, 10, 18, 26, ...
4. Find the 17th term of the arithmetic sequence 5, 8, 11, 14, ...
5. Find the 25th term of the arithmetic sequence 2, 5, 8, 11, ...
6. Find the 9th term of the arithmetic sequence 4, 16, 28, 40, ...
7. Find the 11th term of the arithmetic sequence 25, 36, 47, 58, ...
8. Find the 25th term of the arithmetic sequence 20, 28, 36, 44, ...
9. Find the 17th term of the arithmetic sequence 7, 15, 23, 31, ...
10. Find the 14th term of the arithmetic sequence 10, 15, 20, 25, ...
11. Find the 9th term of the arithmetic sequence 10, 17, 24, 31, ...
12. Find the 11th term of the arithmetic sequence 17, 25, 33, 41, ...

12 questions · Seed 104733 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Linear nth-term sequences

Answers and reasoning. Review before teaching.

1. Find the 23th term of the arithmetic sequence 7, 15, 23, 31, ...
183
First term a = 7 and common difference d = 8. Using a + (n − 1)d gives 7 + 22 × 8 = 183.
2. Find the 8th term of the arithmetic sequence 13, 16, 19, 22, ...
34
First term a = 13 and common difference d = 3. Using a + (n − 1)d gives 13 + 7 × 3 = 34.
3. Find the 13th term of the arithmetic sequence 2, 10, 18, 26, ...
98
First term a = 2 and common difference d = 8. Using a + (n − 1)d gives 2 + 12 × 8 = 98.
4. Find the 17th term of the arithmetic sequence 5, 8, 11, 14, ...
53
First term a = 5 and common difference d = 3. Using a + (n − 1)d gives 5 + 16 × 3 = 53.
5. Find the 25th term of the arithmetic sequence 2, 5, 8, 11, ...
74
First term a = 2 and common difference d = 3. Using a + (n − 1)d gives 2 + 24 × 3 = 74.
6. Find the 9th term of the arithmetic sequence 4, 16, 28, 40, ...
100
First term a = 4 and common difference d = 12. Using a + (n − 1)d gives 4 + 8 × 12 = 100.
7. Find the 11th term of the arithmetic sequence 25, 36, 47, 58, ...
135
First term a = 25 and common difference d = 11. Using a + (n − 1)d gives 25 + 10 × 11 = 135.
8. Find the 25th term of the arithmetic sequence 20, 28, 36, 44, ...
212
First term a = 20 and common difference d = 8. Using a + (n − 1)d gives 20 + 24 × 8 = 212.
9. Find the 17th term of the arithmetic sequence 7, 15, 23, 31, ...
135
First term a = 7 and common difference d = 8. Using a + (n − 1)d gives 7 + 16 × 8 = 135.
10. Find the 14th term of the arithmetic sequence 10, 15, 20, 25, ...
75
First term a = 10 and common difference d = 5. Using a + (n − 1)d gives 10 + 13 × 5 = 75.
11. Find the 9th term of the arithmetic sequence 10, 17, 24, 31, ...
66
First term a = 10 and common difference d = 7. Using a + (n − 1)d gives 10 + 8 × 7 = 66.
12. Find the 11th term of the arithmetic sequence 17, 25, 33, 41, ...
97
First term a = 17 and common difference d = 8. Using a + (n − 1)d gives 17 + 10 × 8 = 97.

12 questions · Seed 104733 · Age guidance, not curriculum certification