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 19th term of the arithmetic sequence 13, 25, 37, 49, ...
2. Find the 11th term of the arithmetic sequence 4, 11, 18, 25, ...
3. Find the 12th term of the arithmetic sequence 10, 17, 24, 31, ...
4. Find the 15th term of the arithmetic sequence 15, 25, 35, 45, ...
5. Find the 15th term of the arithmetic sequence 11, 17, 23, 29, ...
6. Find the 22th term of the arithmetic sequence 2, 14, 26, 38, ...
7. Find the 21th term of the arithmetic sequence 16, 22, 28, 34, ...
8. Find the 12th term of the arithmetic sequence 8, 19, 30, 41, ...
9. Find the 16th term of the arithmetic sequence 14, 19, 24, 29, ...
10. Find the 18th term of the arithmetic sequence 15, 25, 35, 45, ...
11. Find the 13th term of the arithmetic sequence 7, 10, 13, 16, ...
12. Find the 11th term of the arithmetic sequence 5, 7, 9, 11, ...

12 questions · Seed 104732 · 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 19th term of the arithmetic sequence 13, 25, 37, 49, ...
229
First term a = 13 and common difference d = 12. Using a + (n − 1)d gives 13 + 18 × 12 = 229.
2. 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.
3. Find the 12th term of the arithmetic sequence 10, 17, 24, 31, ...
87
First term a = 10 and common difference d = 7. Using a + (n − 1)d gives 10 + 11 × 7 = 87.
4. Find the 15th term of the arithmetic sequence 15, 25, 35, 45, ...
155
First term a = 15 and common difference d = 10. Using a + (n − 1)d gives 15 + 14 × 10 = 155.
5. Find the 15th term of the arithmetic sequence 11, 17, 23, 29, ...
95
First term a = 11 and common difference d = 6. Using a + (n − 1)d gives 11 + 14 × 6 = 95.
6. Find the 22th term of the arithmetic sequence 2, 14, 26, 38, ...
254
First term a = 2 and common difference d = 12. Using a + (n − 1)d gives 2 + 21 × 12 = 254.
7. Find the 21th term of the arithmetic sequence 16, 22, 28, 34, ...
136
First term a = 16 and common difference d = 6. Using a + (n − 1)d gives 16 + 20 × 6 = 136.
8. Find the 12th term of the arithmetic sequence 8, 19, 30, 41, ...
129
First term a = 8 and common difference d = 11. Using a + (n − 1)d gives 8 + 11 × 11 = 129.
9. Find the 16th term of the arithmetic sequence 14, 19, 24, 29, ...
89
First term a = 14 and common difference d = 5. Using a + (n − 1)d gives 14 + 15 × 5 = 89.
10. Find the 18th term of the arithmetic sequence 15, 25, 35, 45, ...
185
First term a = 15 and common difference d = 10. Using a + (n − 1)d gives 15 + 17 × 10 = 185.
11. Find the 13th term of the arithmetic sequence 7, 10, 13, 16, ...
43
First term a = 7 and common difference d = 3. Using a + (n − 1)d gives 7 + 12 × 3 = 43.
12. Find the 11th term of the arithmetic sequence 5, 7, 9, 11, ...
25
First term a = 5 and common difference d = 2. Using a + (n − 1)d gives 5 + 10 × 2 = 25.

12 questions · Seed 104732 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Linear nth-term sequences

Take your time. Show your thinking.

1. Find the 19th term of the arithmetic sequence 13, 25, 37, 49, ...
2. Find the 11th term of the arithmetic sequence 4, 11, 18, 25, ...
3. Find the 12th term of the arithmetic sequence 10, 17, 24, 31, ...
4. Find the 15th term of the arithmetic sequence 15, 25, 35, 45, ...
5. Find the 15th term of the arithmetic sequence 11, 17, 23, 29, ...
6. Find the 22th term of the arithmetic sequence 2, 14, 26, 38, ...
7. Find the 21th term of the arithmetic sequence 16, 22, 28, 34, ...
8. Find the 12th term of the arithmetic sequence 8, 19, 30, 41, ...
9. Find the 16th term of the arithmetic sequence 14, 19, 24, 29, ...
10. Find the 18th term of the arithmetic sequence 15, 25, 35, 45, ...
11. Find the 13th term of the arithmetic sequence 7, 10, 13, 16, ...
12. Find the 11th term of the arithmetic sequence 5, 7, 9, 11, ...

12 questions · Seed 104732 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Linear nth-term sequences

Answers and reasoning. Review before teaching.

1. Find the 19th term of the arithmetic sequence 13, 25, 37, 49, ...
229
First term a = 13 and common difference d = 12. Using a + (n − 1)d gives 13 + 18 × 12 = 229.
2. 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.
3. Find the 12th term of the arithmetic sequence 10, 17, 24, 31, ...
87
First term a = 10 and common difference d = 7. Using a + (n − 1)d gives 10 + 11 × 7 = 87.
4. Find the 15th term of the arithmetic sequence 15, 25, 35, 45, ...
155
First term a = 15 and common difference d = 10. Using a + (n − 1)d gives 15 + 14 × 10 = 155.
5. Find the 15th term of the arithmetic sequence 11, 17, 23, 29, ...
95
First term a = 11 and common difference d = 6. Using a + (n − 1)d gives 11 + 14 × 6 = 95.
6. Find the 22th term of the arithmetic sequence 2, 14, 26, 38, ...
254
First term a = 2 and common difference d = 12. Using a + (n − 1)d gives 2 + 21 × 12 = 254.
7. Find the 21th term of the arithmetic sequence 16, 22, 28, 34, ...
136
First term a = 16 and common difference d = 6. Using a + (n − 1)d gives 16 + 20 × 6 = 136.
8. Find the 12th term of the arithmetic sequence 8, 19, 30, 41, ...
129
First term a = 8 and common difference d = 11. Using a + (n − 1)d gives 8 + 11 × 11 = 129.
9. Find the 16th term of the arithmetic sequence 14, 19, 24, 29, ...
89
First term a = 14 and common difference d = 5. Using a + (n − 1)d gives 14 + 15 × 5 = 89.
10. Find the 18th term of the arithmetic sequence 15, 25, 35, 45, ...
185
First term a = 15 and common difference d = 10. Using a + (n − 1)d gives 15 + 17 × 10 = 185.
11. Find the 13th term of the arithmetic sequence 7, 10, 13, 16, ...
43
First term a = 7 and common difference d = 3. Using a + (n − 1)d gives 7 + 12 × 3 = 43.
12. Find the 11th term of the arithmetic sequence 5, 7, 9, 11, ...
25
First term a = 5 and common difference d = 2. Using a + (n − 1)d gives 5 + 10 × 2 = 25.

12 questions · Seed 104732 · Age guidance, not curriculum certification