ReasoningAges 16-18

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 16-18

Linear nth-term sequences

Take your time. Show your thinking.

1. Find the 20th term of the arithmetic sequence 25, 32, 39, 46, ...
2. Find the 25th term of the arithmetic sequence 19, 22, 25, 28, ...
3. Find the 12th term of the arithmetic sequence 15, 17, 19, 21, ...
4. Find the 17th term of the arithmetic sequence 9, 15, 21, 27, ...
5. Find the 22th term of the arithmetic sequence 6, 14, 22, 30, ...
6. Find the 23th term of the arithmetic sequence 7, 14, 21, 28, ...
7. Find the 19th term of the arithmetic sequence 9, 18, 27, 36, ...
8. Find the 25th term of the arithmetic sequence 18, 21, 24, 27, ...
9. Find the 23th term of the arithmetic sequence 25, 32, 39, 46, ...
10. Find the 22th term of the arithmetic sequence 18, 27, 36, 45, ...
11. Find the 14th term of the arithmetic sequence 24, 36, 48, 60, ...
12. Find the 25th term of the arithmetic sequence 10, 19, 28, 37, ...

12 questions · Seed 104738 · Age guidance, not curriculum certification

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Worksheet StudioAnswer key · Ages 16-18

Linear nth-term sequences

Answers and reasoning. Review before teaching.

1. Find the 20th term of the arithmetic sequence 25, 32, 39, 46, ...
158
First term a = 25 and common difference d = 7. Using a + (n − 1)d gives 25 + 19 × 7 = 158.
2. Find the 25th term of the arithmetic sequence 19, 22, 25, 28, ...
91
First term a = 19 and common difference d = 3. Using a + (n − 1)d gives 19 + 24 × 3 = 91.
3. Find the 12th term of the arithmetic sequence 15, 17, 19, 21, ...
37
First term a = 15 and common difference d = 2. Using a + (n − 1)d gives 15 + 11 × 2 = 37.
4. Find the 17th term of the arithmetic sequence 9, 15, 21, 27, ...
105
First term a = 9 and common difference d = 6. Using a + (n − 1)d gives 9 + 16 × 6 = 105.
5. Find the 22th term of the arithmetic sequence 6, 14, 22, 30, ...
174
First term a = 6 and common difference d = 8. Using a + (n − 1)d gives 6 + 21 × 8 = 174.
6. Find the 23th term of the arithmetic sequence 7, 14, 21, 28, ...
161
First term a = 7 and common difference d = 7. Using a + (n − 1)d gives 7 + 22 × 7 = 161.
7. Find the 19th term of the arithmetic sequence 9, 18, 27, 36, ...
171
First term a = 9 and common difference d = 9. Using a + (n − 1)d gives 9 + 18 × 9 = 171.
8. Find the 25th term of the arithmetic sequence 18, 21, 24, 27, ...
90
First term a = 18 and common difference d = 3. Using a + (n − 1)d gives 18 + 24 × 3 = 90.
9. Find the 23th term of the arithmetic sequence 25, 32, 39, 46, ...
179
First term a = 25 and common difference d = 7. Using a + (n − 1)d gives 25 + 22 × 7 = 179.
10. Find the 22th term of the arithmetic sequence 18, 27, 36, 45, ...
207
First term a = 18 and common difference d = 9. Using a + (n − 1)d gives 18 + 21 × 9 = 207.
11. Find the 14th term of the arithmetic sequence 24, 36, 48, 60, ...
180
First term a = 24 and common difference d = 12. Using a + (n − 1)d gives 24 + 13 × 12 = 180.
12. Find the 25th term of the arithmetic sequence 10, 19, 28, 37, ...
226
First term a = 10 and common difference d = 9. Using a + (n − 1)d gives 10 + 24 × 9 = 226.

12 questions · Seed 104738 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Linear nth-term sequences

Take your time. Show your thinking.

1. Find the 20th term of the arithmetic sequence 25, 32, 39, 46, ...
2. Find the 25th term of the arithmetic sequence 19, 22, 25, 28, ...
3. Find the 12th term of the arithmetic sequence 15, 17, 19, 21, ...
4. Find the 17th term of the arithmetic sequence 9, 15, 21, 27, ...
5. Find the 22th term of the arithmetic sequence 6, 14, 22, 30, ...
6. Find the 23th term of the arithmetic sequence 7, 14, 21, 28, ...
7. Find the 19th term of the arithmetic sequence 9, 18, 27, 36, ...
8. Find the 25th term of the arithmetic sequence 18, 21, 24, 27, ...
9. Find the 23th term of the arithmetic sequence 25, 32, 39, 46, ...
10. Find the 22th term of the arithmetic sequence 18, 27, 36, 45, ...
11. Find the 14th term of the arithmetic sequence 24, 36, 48, 60, ...
12. Find the 25th term of the arithmetic sequence 10, 19, 28, 37, ...

12 questions · Seed 104738 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Linear nth-term sequences

Answers and reasoning. Review before teaching.

1. Find the 20th term of the arithmetic sequence 25, 32, 39, 46, ...
158
First term a = 25 and common difference d = 7. Using a + (n − 1)d gives 25 + 19 × 7 = 158.
2. Find the 25th term of the arithmetic sequence 19, 22, 25, 28, ...
91
First term a = 19 and common difference d = 3. Using a + (n − 1)d gives 19 + 24 × 3 = 91.
3. Find the 12th term of the arithmetic sequence 15, 17, 19, 21, ...
37
First term a = 15 and common difference d = 2. Using a + (n − 1)d gives 15 + 11 × 2 = 37.
4. Find the 17th term of the arithmetic sequence 9, 15, 21, 27, ...
105
First term a = 9 and common difference d = 6. Using a + (n − 1)d gives 9 + 16 × 6 = 105.
5. Find the 22th term of the arithmetic sequence 6, 14, 22, 30, ...
174
First term a = 6 and common difference d = 8. Using a + (n − 1)d gives 6 + 21 × 8 = 174.
6. Find the 23th term of the arithmetic sequence 7, 14, 21, 28, ...
161
First term a = 7 and common difference d = 7. Using a + (n − 1)d gives 7 + 22 × 7 = 161.
7. Find the 19th term of the arithmetic sequence 9, 18, 27, 36, ...
171
First term a = 9 and common difference d = 9. Using a + (n − 1)d gives 9 + 18 × 9 = 171.
8. Find the 25th term of the arithmetic sequence 18, 21, 24, 27, ...
90
First term a = 18 and common difference d = 3. Using a + (n − 1)d gives 18 + 24 × 3 = 90.
9. Find the 23th term of the arithmetic sequence 25, 32, 39, 46, ...
179
First term a = 25 and common difference d = 7. Using a + (n − 1)d gives 25 + 22 × 7 = 179.
10. Find the 22th term of the arithmetic sequence 18, 27, 36, 45, ...
207
First term a = 18 and common difference d = 9. Using a + (n − 1)d gives 18 + 21 × 9 = 207.
11. Find the 14th term of the arithmetic sequence 24, 36, 48, 60, ...
180
First term a = 24 and common difference d = 12. Using a + (n − 1)d gives 24 + 13 × 12 = 180.
12. Find the 25th term of the arithmetic sequence 10, 19, 28, 37, ...
226
First term a = 10 and common difference d = 9. Using a + (n − 1)d gives 10 + 24 × 9 = 226.

12 questions · Seed 104738 · Age guidance, not curriculum certification