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 18th term of the arithmetic sequence 15, 18, 21, 24, ...
2. Find the 10th term of the arithmetic sequence 14, 23, 32, 41, ...
3. Find the 10th term of the arithmetic sequence 17, 29, 41, 53, ...
4. Find the 9th term of the arithmetic sequence 5, 13, 21, 29, ...
5. Find the 16th term of the arithmetic sequence 16, 26, 36, 46, ...
6. Find the 11th term of the arithmetic sequence 4, 11, 18, 25, ...
7. Find the 18th term of the arithmetic sequence 21, 33, 45, 57, ...
8. Find the 14th term of the arithmetic sequence 14, 20, 26, 32, ...
9. Find the 21th term of the arithmetic sequence 24, 36, 48, 60, ...
10. Find the 16th term of the arithmetic sequence 6, 18, 30, 42, ...
11. Find the 10th term of the arithmetic sequence 25, 31, 37, 43, ...
12. Find the 17th term of the arithmetic sequence 10, 19, 28, 37, ...

12 questions · Seed 51 · 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 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.
2. Find the 10th term of the arithmetic sequence 14, 23, 32, 41, ...
95
First term a = 14 and common difference d = 9. Using a + (n − 1)d gives 14 + 9 × 9 = 95.
3. Find the 10th term of the arithmetic sequence 17, 29, 41, 53, ...
125
First term a = 17 and common difference d = 12. Using a + (n − 1)d gives 17 + 9 × 12 = 125.
4. Find the 9th term of the arithmetic sequence 5, 13, 21, 29, ...
69
First term a = 5 and common difference d = 8. Using a + (n − 1)d gives 5 + 8 × 8 = 69.
5. Find the 16th term of the arithmetic sequence 16, 26, 36, 46, ...
166
First term a = 16 and common difference d = 10. Using a + (n − 1)d gives 16 + 15 × 10 = 166.
6. Find the 11th term of the arithmetic sequence 4, 11, 18, 25, ...
74
First term a = 4 and common difference d = 7. Using a + (n − 1)d gives 4 + 10 × 7 = 74.
7. Find the 18th term of the arithmetic sequence 21, 33, 45, 57, ...
225
First term a = 21 and common difference d = 12. Using a + (n − 1)d gives 21 + 17 × 12 = 225.
8. Find the 14th term of the arithmetic sequence 14, 20, 26, 32, ...
92
First term a = 14 and common difference d = 6. Using a + (n − 1)d gives 14 + 13 × 6 = 92.
9. Find the 21th term of the arithmetic sequence 24, 36, 48, 60, ...
264
First term a = 24 and common difference d = 12. Using a + (n − 1)d gives 24 + 20 × 12 = 264.
10. Find the 16th term of the arithmetic sequence 6, 18, 30, 42, ...
186
First term a = 6 and common difference d = 12. Using a + (n − 1)d gives 6 + 15 × 12 = 186.
11. Find the 10th term of the arithmetic sequence 25, 31, 37, 43, ...
79
First term a = 25 and common difference d = 6. Using a + (n − 1)d gives 25 + 9 × 6 = 79.
12. Find the 17th term of the arithmetic sequence 10, 19, 28, 37, ...
154
First term a = 10 and common difference d = 9. Using a + (n − 1)d gives 10 + 16 × 9 = 154.

12 questions · Seed 51 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Linear nth-term sequences

Take your time. Show your thinking.

1. Find the 18th term of the arithmetic sequence 15, 18, 21, 24, ...
2. Find the 10th term of the arithmetic sequence 14, 23, 32, 41, ...
3. Find the 10th term of the arithmetic sequence 17, 29, 41, 53, ...
4. Find the 9th term of the arithmetic sequence 5, 13, 21, 29, ...
5. Find the 16th term of the arithmetic sequence 16, 26, 36, 46, ...
6. Find the 11th term of the arithmetic sequence 4, 11, 18, 25, ...
7. Find the 18th term of the arithmetic sequence 21, 33, 45, 57, ...
8. Find the 14th term of the arithmetic sequence 14, 20, 26, 32, ...
9. Find the 21th term of the arithmetic sequence 24, 36, 48, 60, ...
10. Find the 16th term of the arithmetic sequence 6, 18, 30, 42, ...
11. Find the 10th term of the arithmetic sequence 25, 31, 37, 43, ...
12. Find the 17th term of the arithmetic sequence 10, 19, 28, 37, ...

12 questions · Seed 51 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Linear nth-term sequences

Answers and reasoning. Review before teaching.

1. 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.
2. Find the 10th term of the arithmetic sequence 14, 23, 32, 41, ...
95
First term a = 14 and common difference d = 9. Using a + (n − 1)d gives 14 + 9 × 9 = 95.
3. Find the 10th term of the arithmetic sequence 17, 29, 41, 53, ...
125
First term a = 17 and common difference d = 12. Using a + (n − 1)d gives 17 + 9 × 12 = 125.
4. Find the 9th term of the arithmetic sequence 5, 13, 21, 29, ...
69
First term a = 5 and common difference d = 8. Using a + (n − 1)d gives 5 + 8 × 8 = 69.
5. Find the 16th term of the arithmetic sequence 16, 26, 36, 46, ...
166
First term a = 16 and common difference d = 10. Using a + (n − 1)d gives 16 + 15 × 10 = 166.
6. Find the 11th term of the arithmetic sequence 4, 11, 18, 25, ...
74
First term a = 4 and common difference d = 7. Using a + (n − 1)d gives 4 + 10 × 7 = 74.
7. Find the 18th term of the arithmetic sequence 21, 33, 45, 57, ...
225
First term a = 21 and common difference d = 12. Using a + (n − 1)d gives 21 + 17 × 12 = 225.
8. Find the 14th term of the arithmetic sequence 14, 20, 26, 32, ...
92
First term a = 14 and common difference d = 6. Using a + (n − 1)d gives 14 + 13 × 6 = 92.
9. Find the 21th term of the arithmetic sequence 24, 36, 48, 60, ...
264
First term a = 24 and common difference d = 12. Using a + (n − 1)d gives 24 + 20 × 12 = 264.
10. Find the 16th term of the arithmetic sequence 6, 18, 30, 42, ...
186
First term a = 6 and common difference d = 12. Using a + (n − 1)d gives 6 + 15 × 12 = 186.
11. Find the 10th term of the arithmetic sequence 25, 31, 37, 43, ...
79
First term a = 25 and common difference d = 6. Using a + (n − 1)d gives 25 + 9 × 6 = 79.
12. Find the 17th term of the arithmetic sequence 10, 19, 28, 37, ...
154
First term a = 10 and common difference d = 9. Using a + (n − 1)d gives 10 + 16 × 9 = 154.

12 questions · Seed 51 · Age guidance, not curriculum certification