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 8th term of the arithmetic sequence 12, 15, 18, 21, ...
2. Find the 13th term of the arithmetic sequence 9, 14, 19, 24, ...
3. Find the 19th term of the arithmetic sequence 4, 14, 24, 34, ...
4. Find the 16th term of the arithmetic sequence 25, 36, 47, 58, ...
5. Find the 12th term of the arithmetic sequence 17, 28, 39, 50, ...
6. Find the 10th term of the arithmetic sequence 20, 28, 36, 44, ...
7. Find the 10th term of the arithmetic sequence 8, 19, 30, 41, ...
8. Find the 12th term of the arithmetic sequence 7, 11, 15, 19, ...
9. Find the 17th term of the arithmetic sequence 13, 15, 17, 19, ...
10. Find the 13th term of the arithmetic sequence 25, 28, 31, 34, ...
11. Find the 15th term of the arithmetic sequence 13, 20, 27, 34, ...
12. Find the 8th term of the arithmetic sequence 4, 7, 10, 13, ...

12 questions · Seed 43 · 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 8th term of the arithmetic sequence 12, 15, 18, 21, ...
33
First term a = 12 and common difference d = 3. Using a + (n − 1)d gives 12 + 7 × 3 = 33.
2. Find the 13th term of the arithmetic sequence 9, 14, 19, 24, ...
69
First term a = 9 and common difference d = 5. Using a + (n − 1)d gives 9 + 12 × 5 = 69.
3. Find the 19th term of the arithmetic sequence 4, 14, 24, 34, ...
184
First term a = 4 and common difference d = 10. Using a + (n − 1)d gives 4 + 18 × 10 = 184.
4. Find the 16th term of the arithmetic sequence 25, 36, 47, 58, ...
190
First term a = 25 and common difference d = 11. Using a + (n − 1)d gives 25 + 15 × 11 = 190.
5. Find the 12th term of the arithmetic sequence 17, 28, 39, 50, ...
138
First term a = 17 and common difference d = 11. Using a + (n − 1)d gives 17 + 11 × 11 = 138.
6. Find the 10th term of the arithmetic sequence 20, 28, 36, 44, ...
92
First term a = 20 and common difference d = 8. Using a + (n − 1)d gives 20 + 9 × 8 = 92.
7. Find the 10th term of the arithmetic sequence 8, 19, 30, 41, ...
107
First term a = 8 and common difference d = 11. Using a + (n − 1)d gives 8 + 9 × 11 = 107.
8. Find the 12th term of the arithmetic sequence 7, 11, 15, 19, ...
51
First term a = 7 and common difference d = 4. Using a + (n − 1)d gives 7 + 11 × 4 = 51.
9. Find the 17th term of the arithmetic sequence 13, 15, 17, 19, ...
45
First term a = 13 and common difference d = 2. Using a + (n − 1)d gives 13 + 16 × 2 = 45.
10. Find the 13th term of the arithmetic sequence 25, 28, 31, 34, ...
61
First term a = 25 and common difference d = 3. Using a + (n − 1)d gives 25 + 12 × 3 = 61.
11. Find the 15th term of the arithmetic sequence 13, 20, 27, 34, ...
111
First term a = 13 and common difference d = 7. Using a + (n − 1)d gives 13 + 14 × 7 = 111.
12. Find the 8th term of the arithmetic sequence 4, 7, 10, 13, ...
25
First term a = 4 and common difference d = 3. Using a + (n − 1)d gives 4 + 7 × 3 = 25.

12 questions · Seed 43 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Linear nth-term sequences

Take your time. Show your thinking.

1. Find the 8th term of the arithmetic sequence 12, 15, 18, 21, ...
2. Find the 13th term of the arithmetic sequence 9, 14, 19, 24, ...
3. Find the 19th term of the arithmetic sequence 4, 14, 24, 34, ...
4. Find the 16th term of the arithmetic sequence 25, 36, 47, 58, ...
5. Find the 12th term of the arithmetic sequence 17, 28, 39, 50, ...
6. Find the 10th term of the arithmetic sequence 20, 28, 36, 44, ...
7. Find the 10th term of the arithmetic sequence 8, 19, 30, 41, ...
8. Find the 12th term of the arithmetic sequence 7, 11, 15, 19, ...
9. Find the 17th term of the arithmetic sequence 13, 15, 17, 19, ...
10. Find the 13th term of the arithmetic sequence 25, 28, 31, 34, ...
11. Find the 15th term of the arithmetic sequence 13, 20, 27, 34, ...
12. Find the 8th term of the arithmetic sequence 4, 7, 10, 13, ...

12 questions · Seed 43 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Linear nth-term sequences

Answers and reasoning. Review before teaching.

1. Find the 8th term of the arithmetic sequence 12, 15, 18, 21, ...
33
First term a = 12 and common difference d = 3. Using a + (n − 1)d gives 12 + 7 × 3 = 33.
2. Find the 13th term of the arithmetic sequence 9, 14, 19, 24, ...
69
First term a = 9 and common difference d = 5. Using a + (n − 1)d gives 9 + 12 × 5 = 69.
3. Find the 19th term of the arithmetic sequence 4, 14, 24, 34, ...
184
First term a = 4 and common difference d = 10. Using a + (n − 1)d gives 4 + 18 × 10 = 184.
4. Find the 16th term of the arithmetic sequence 25, 36, 47, 58, ...
190
First term a = 25 and common difference d = 11. Using a + (n − 1)d gives 25 + 15 × 11 = 190.
5. Find the 12th term of the arithmetic sequence 17, 28, 39, 50, ...
138
First term a = 17 and common difference d = 11. Using a + (n − 1)d gives 17 + 11 × 11 = 138.
6. Find the 10th term of the arithmetic sequence 20, 28, 36, 44, ...
92
First term a = 20 and common difference d = 8. Using a + (n − 1)d gives 20 + 9 × 8 = 92.
7. Find the 10th term of the arithmetic sequence 8, 19, 30, 41, ...
107
First term a = 8 and common difference d = 11. Using a + (n − 1)d gives 8 + 9 × 11 = 107.
8. Find the 12th term of the arithmetic sequence 7, 11, 15, 19, ...
51
First term a = 7 and common difference d = 4. Using a + (n − 1)d gives 7 + 11 × 4 = 51.
9. Find the 17th term of the arithmetic sequence 13, 15, 17, 19, ...
45
First term a = 13 and common difference d = 2. Using a + (n − 1)d gives 13 + 16 × 2 = 45.
10. Find the 13th term of the arithmetic sequence 25, 28, 31, 34, ...
61
First term a = 25 and common difference d = 3. Using a + (n − 1)d gives 25 + 12 × 3 = 61.
11. Find the 15th term of the arithmetic sequence 13, 20, 27, 34, ...
111
First term a = 13 and common difference d = 7. Using a + (n − 1)d gives 13 + 14 × 7 = 111.
12. Find the 8th term of the arithmetic sequence 4, 7, 10, 13, ...
25
First term a = 4 and common difference d = 3. Using a + (n − 1)d gives 4 + 7 × 3 = 25.

12 questions · Seed 43 · Age guidance, not curriculum certification