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 12th term of the arithmetic sequence 20, 25, 30, 35, ...
2. Find the 14th term of the arithmetic sequence 20, 26, 32, 38, ...
3. Find the 15th term of the arithmetic sequence 17, 29, 41, 53, ...
4. Find the 19th term of the arithmetic sequence 7, 17, 27, 37, ...
5. Find the 10th term of the arithmetic sequence 11, 22, 33, 44, ...
6. Find the 22th term of the arithmetic sequence 19, 25, 31, 37, ...
7. Find the 16th term of the arithmetic sequence 24, 28, 32, 36, ...
8. Find the 15th term of the arithmetic sequence 3, 15, 27, 39, ...
9. Find the 25th term of the arithmetic sequence 18, 29, 40, 51, ...
10. Find the 21th term of the arithmetic sequence 21, 29, 37, 45, ...
11. Find the 23th term of the arithmetic sequence 23, 32, 41, 50, ...
12. Find the 17th term of the arithmetic sequence 4, 6, 8, 10, ...

12 questions · Seed 48 · 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 12th term of the arithmetic sequence 20, 25, 30, 35, ...
75
First term a = 20 and common difference d = 5. Using a + (n − 1)d gives 20 + 11 × 5 = 75.
2. Find the 14th term of the arithmetic sequence 20, 26, 32, 38, ...
98
First term a = 20 and common difference d = 6. Using a + (n − 1)d gives 20 + 13 × 6 = 98.
3. Find the 15th term of the arithmetic sequence 17, 29, 41, 53, ...
185
First term a = 17 and common difference d = 12. Using a + (n − 1)d gives 17 + 14 × 12 = 185.
4. Find the 19th term of the arithmetic sequence 7, 17, 27, 37, ...
187
First term a = 7 and common difference d = 10. Using a + (n − 1)d gives 7 + 18 × 10 = 187.
5. Find the 10th term of the arithmetic sequence 11, 22, 33, 44, ...
110
First term a = 11 and common difference d = 11. Using a + (n − 1)d gives 11 + 9 × 11 = 110.
6. Find the 22th term of the arithmetic sequence 19, 25, 31, 37, ...
145
First term a = 19 and common difference d = 6. Using a + (n − 1)d gives 19 + 21 × 6 = 145.
7. Find the 16th term of the arithmetic sequence 24, 28, 32, 36, ...
84
First term a = 24 and common difference d = 4. Using a + (n − 1)d gives 24 + 15 × 4 = 84.
8. Find the 15th term of the arithmetic sequence 3, 15, 27, 39, ...
171
First term a = 3 and common difference d = 12. Using a + (n − 1)d gives 3 + 14 × 12 = 171.
9. Find the 25th term of the arithmetic sequence 18, 29, 40, 51, ...
282
First term a = 18 and common difference d = 11. Using a + (n − 1)d gives 18 + 24 × 11 = 282.
10. Find the 21th term of the arithmetic sequence 21, 29, 37, 45, ...
181
First term a = 21 and common difference d = 8. Using a + (n − 1)d gives 21 + 20 × 8 = 181.
11. Find the 23th term of the arithmetic sequence 23, 32, 41, 50, ...
221
First term a = 23 and common difference d = 9. Using a + (n − 1)d gives 23 + 22 × 9 = 221.
12. Find the 17th term of the arithmetic sequence 4, 6, 8, 10, ...
36
First term a = 4 and common difference d = 2. Using a + (n − 1)d gives 4 + 16 × 2 = 36.

12 questions · Seed 48 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Linear nth-term sequences

Take your time. Show your thinking.

1. Find the 12th term of the arithmetic sequence 20, 25, 30, 35, ...
2. Find the 14th term of the arithmetic sequence 20, 26, 32, 38, ...
3. Find the 15th term of the arithmetic sequence 17, 29, 41, 53, ...
4. Find the 19th term of the arithmetic sequence 7, 17, 27, 37, ...
5. Find the 10th term of the arithmetic sequence 11, 22, 33, 44, ...
6. Find the 22th term of the arithmetic sequence 19, 25, 31, 37, ...
7. Find the 16th term of the arithmetic sequence 24, 28, 32, 36, ...
8. Find the 15th term of the arithmetic sequence 3, 15, 27, 39, ...
9. Find the 25th term of the arithmetic sequence 18, 29, 40, 51, ...
10. Find the 21th term of the arithmetic sequence 21, 29, 37, 45, ...
11. Find the 23th term of the arithmetic sequence 23, 32, 41, 50, ...
12. Find the 17th term of the arithmetic sequence 4, 6, 8, 10, ...

12 questions · Seed 48 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Linear nth-term sequences

Answers and reasoning. Review before teaching.

1. Find the 12th term of the arithmetic sequence 20, 25, 30, 35, ...
75
First term a = 20 and common difference d = 5. Using a + (n − 1)d gives 20 + 11 × 5 = 75.
2. Find the 14th term of the arithmetic sequence 20, 26, 32, 38, ...
98
First term a = 20 and common difference d = 6. Using a + (n − 1)d gives 20 + 13 × 6 = 98.
3. Find the 15th term of the arithmetic sequence 17, 29, 41, 53, ...
185
First term a = 17 and common difference d = 12. Using a + (n − 1)d gives 17 + 14 × 12 = 185.
4. Find the 19th term of the arithmetic sequence 7, 17, 27, 37, ...
187
First term a = 7 and common difference d = 10. Using a + (n − 1)d gives 7 + 18 × 10 = 187.
5. Find the 10th term of the arithmetic sequence 11, 22, 33, 44, ...
110
First term a = 11 and common difference d = 11. Using a + (n − 1)d gives 11 + 9 × 11 = 110.
6. Find the 22th term of the arithmetic sequence 19, 25, 31, 37, ...
145
First term a = 19 and common difference d = 6. Using a + (n − 1)d gives 19 + 21 × 6 = 145.
7. Find the 16th term of the arithmetic sequence 24, 28, 32, 36, ...
84
First term a = 24 and common difference d = 4. Using a + (n − 1)d gives 24 + 15 × 4 = 84.
8. Find the 15th term of the arithmetic sequence 3, 15, 27, 39, ...
171
First term a = 3 and common difference d = 12. Using a + (n − 1)d gives 3 + 14 × 12 = 171.
9. Find the 25th term of the arithmetic sequence 18, 29, 40, 51, ...
282
First term a = 18 and common difference d = 11. Using a + (n − 1)d gives 18 + 24 × 11 = 282.
10. Find the 21th term of the arithmetic sequence 21, 29, 37, 45, ...
181
First term a = 21 and common difference d = 8. Using a + (n − 1)d gives 21 + 20 × 8 = 181.
11. Find the 23th term of the arithmetic sequence 23, 32, 41, 50, ...
221
First term a = 23 and common difference d = 9. Using a + (n − 1)d gives 23 + 22 × 9 = 221.
12. Find the 17th term of the arithmetic sequence 4, 6, 8, 10, ...
36
First term a = 4 and common difference d = 2. Using a + (n − 1)d gives 4 + 16 × 2 = 36.

12 questions · Seed 48 · Age guidance, not curriculum certification