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 17th term of the arithmetic sequence 23, 31, 39, 47, ...
2. Find the 18th term of the arithmetic sequence 19, 21, 23, 25, ...
3. Find the 12th term of the arithmetic sequence 22, 25, 28, 31, ...
4. Find the 18th term of the arithmetic sequence 10, 22, 34, 46, ...
5. Find the 19th term of the arithmetic sequence 12, 19, 26, 33, ...
6. Find the 19th term of the arithmetic sequence 3, 7, 11, 15, ...
7. Find the 22th term of the arithmetic sequence 8, 11, 14, 17, ...
8. Find the 12th term of the arithmetic sequence 10, 15, 20, 25, ...
9. Find the 21th term of the arithmetic sequence 24, 30, 36, 42, ...
10. Find the 16th term of the arithmetic sequence 21, 28, 35, 42, ...
11. Find the 18th term of the arithmetic sequence 15, 18, 21, 24, ...
12. Find the 11th term of the arithmetic sequence 16, 28, 40, 52, ...

12 questions · Seed 104740 · 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 17th term of the arithmetic sequence 23, 31, 39, 47, ...
151
First term a = 23 and common difference d = 8. Using a + (n − 1)d gives 23 + 16 × 8 = 151.
2. Find the 18th term of the arithmetic sequence 19, 21, 23, 25, ...
53
First term a = 19 and common difference d = 2. Using a + (n − 1)d gives 19 + 17 × 2 = 53.
3. Find the 12th term of the arithmetic sequence 22, 25, 28, 31, ...
55
First term a = 22 and common difference d = 3. Using a + (n − 1)d gives 22 + 11 × 3 = 55.
4. Find the 18th term of the arithmetic sequence 10, 22, 34, 46, ...
214
First term a = 10 and common difference d = 12. Using a + (n − 1)d gives 10 + 17 × 12 = 214.
5. Find the 19th term of the arithmetic sequence 12, 19, 26, 33, ...
138
First term a = 12 and common difference d = 7. Using a + (n − 1)d gives 12 + 18 × 7 = 138.
6. Find the 19th term of the arithmetic sequence 3, 7, 11, 15, ...
75
First term a = 3 and common difference d = 4. Using a + (n − 1)d gives 3 + 18 × 4 = 75.
7. Find the 22th term of the arithmetic sequence 8, 11, 14, 17, ...
71
First term a = 8 and common difference d = 3. Using a + (n − 1)d gives 8 + 21 × 3 = 71.
8. Find the 12th term of the arithmetic sequence 10, 15, 20, 25, ...
65
First term a = 10 and common difference d = 5. Using a + (n − 1)d gives 10 + 11 × 5 = 65.
9. Find the 21th term of the arithmetic sequence 24, 30, 36, 42, ...
144
First term a = 24 and common difference d = 6. Using a + (n − 1)d gives 24 + 20 × 6 = 144.
10. Find the 16th term of the arithmetic sequence 21, 28, 35, 42, ...
126
First term a = 21 and common difference d = 7. Using a + (n − 1)d gives 21 + 15 × 7 = 126.
11. Find the 18th term of the arithmetic sequence 15, 18, 21, 24, ...
66
First term a = 15 and common difference d = 3. Using a + (n − 1)d gives 15 + 17 × 3 = 66.
12. Find the 11th term of the arithmetic sequence 16, 28, 40, 52, ...
136
First term a = 16 and common difference d = 12. Using a + (n − 1)d gives 16 + 10 × 12 = 136.

12 questions · Seed 104740 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Linear nth-term sequences

Take your time. Show your thinking.

1. Find the 17th term of the arithmetic sequence 23, 31, 39, 47, ...
2. Find the 18th term of the arithmetic sequence 19, 21, 23, 25, ...
3. Find the 12th term of the arithmetic sequence 22, 25, 28, 31, ...
4. Find the 18th term of the arithmetic sequence 10, 22, 34, 46, ...
5. Find the 19th term of the arithmetic sequence 12, 19, 26, 33, ...
6. Find the 19th term of the arithmetic sequence 3, 7, 11, 15, ...
7. Find the 22th term of the arithmetic sequence 8, 11, 14, 17, ...
8. Find the 12th term of the arithmetic sequence 10, 15, 20, 25, ...
9. Find the 21th term of the arithmetic sequence 24, 30, 36, 42, ...
10. Find the 16th term of the arithmetic sequence 21, 28, 35, 42, ...
11. Find the 18th term of the arithmetic sequence 15, 18, 21, 24, ...
12. Find the 11th term of the arithmetic sequence 16, 28, 40, 52, ...

12 questions · Seed 104740 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Linear nth-term sequences

Answers and reasoning. Review before teaching.

1. Find the 17th term of the arithmetic sequence 23, 31, 39, 47, ...
151
First term a = 23 and common difference d = 8. Using a + (n − 1)d gives 23 + 16 × 8 = 151.
2. Find the 18th term of the arithmetic sequence 19, 21, 23, 25, ...
53
First term a = 19 and common difference d = 2. Using a + (n − 1)d gives 19 + 17 × 2 = 53.
3. Find the 12th term of the arithmetic sequence 22, 25, 28, 31, ...
55
First term a = 22 and common difference d = 3. Using a + (n − 1)d gives 22 + 11 × 3 = 55.
4. Find the 18th term of the arithmetic sequence 10, 22, 34, 46, ...
214
First term a = 10 and common difference d = 12. Using a + (n − 1)d gives 10 + 17 × 12 = 214.
5. Find the 19th term of the arithmetic sequence 12, 19, 26, 33, ...
138
First term a = 12 and common difference d = 7. Using a + (n − 1)d gives 12 + 18 × 7 = 138.
6. Find the 19th term of the arithmetic sequence 3, 7, 11, 15, ...
75
First term a = 3 and common difference d = 4. Using a + (n − 1)d gives 3 + 18 × 4 = 75.
7. Find the 22th term of the arithmetic sequence 8, 11, 14, 17, ...
71
First term a = 8 and common difference d = 3. Using a + (n − 1)d gives 8 + 21 × 3 = 71.
8. Find the 12th term of the arithmetic sequence 10, 15, 20, 25, ...
65
First term a = 10 and common difference d = 5. Using a + (n − 1)d gives 10 + 11 × 5 = 65.
9. Find the 21th term of the arithmetic sequence 24, 30, 36, 42, ...
144
First term a = 24 and common difference d = 6. Using a + (n − 1)d gives 24 + 20 × 6 = 144.
10. Find the 16th term of the arithmetic sequence 21, 28, 35, 42, ...
126
First term a = 21 and common difference d = 7. Using a + (n − 1)d gives 21 + 15 × 7 = 126.
11. Find the 18th term of the arithmetic sequence 15, 18, 21, 24, ...
66
First term a = 15 and common difference d = 3. Using a + (n − 1)d gives 15 + 17 × 3 = 66.
12. Find the 11th term of the arithmetic sequence 16, 28, 40, 52, ...
136
First term a = 16 and common difference d = 12. Using a + (n − 1)d gives 16 + 10 × 12 = 136.

12 questions · Seed 104740 · Age guidance, not curriculum certification