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.

New variation Try interactive challenge Browse templates

Age band:Ages 13-15 Ages 16-18

Choose “Save as PDF” to keep a copy. Use your browser’s paper setting for A4 or Letter.

Worksheet StudioPractice pack · Ages 13-15

Linear nth-term sequences

Take your time. Show your thinking.

1. Find the 19th term of the arithmetic sequence 10, 17, 24, 31, ...
2. Find the 14th term of the arithmetic sequence 10, 22, 34, 46, ...
3. Find the 16th term of the arithmetic sequence 13, 22, 31, 40, ...
4. Find the 16th term of the arithmetic sequence 15, 19, 23, 27, ...
5. Find the 16th term of the arithmetic sequence 23, 29, 35, 41, ...
6. Find the 16th term of the arithmetic sequence 22, 25, 28, 31, ...
7. Find the 25th term of the arithmetic sequence 14, 22, 30, 38, ...
8. Find the 25th term of the arithmetic sequence 4, 14, 24, 34, ...
9. Find the 17th term of the arithmetic sequence 17, 21, 25, 29, ...
10. Find the 17th term of the arithmetic sequence 10, 22, 34, 46, ...
11. Find the 14th term of the arithmetic sequence 11, 20, 29, 38, ...
12. Find the 8th term of the arithmetic sequence 6, 16, 26, 36, ...

12 questions · Seed 104741 · 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 19th term of the arithmetic sequence 10, 17, 24, 31, ...
136
First term a = 10 and common difference d = 7. Using a + (n − 1)d gives 10 + 18 × 7 = 136.
2. Find the 14th term of the arithmetic sequence 10, 22, 34, 46, ...
166
First term a = 10 and common difference d = 12. Using a + (n − 1)d gives 10 + 13 × 12 = 166.
3. Find the 16th term of the arithmetic sequence 13, 22, 31, 40, ...
148
First term a = 13 and common difference d = 9. Using a + (n − 1)d gives 13 + 15 × 9 = 148.
4. Find the 16th term of the arithmetic sequence 15, 19, 23, 27, ...
75
First term a = 15 and common difference d = 4. Using a + (n − 1)d gives 15 + 15 × 4 = 75.
5. Find the 16th term of the arithmetic sequence 23, 29, 35, 41, ...
113
First term a = 23 and common difference d = 6. Using a + (n − 1)d gives 23 + 15 × 6 = 113.
6. Find the 16th term of the arithmetic sequence 22, 25, 28, 31, ...
67
First term a = 22 and common difference d = 3. Using a + (n − 1)d gives 22 + 15 × 3 = 67.
7. Find the 25th term of the arithmetic sequence 14, 22, 30, 38, ...
206
First term a = 14 and common difference d = 8. Using a + (n − 1)d gives 14 + 24 × 8 = 206.
8. Find the 25th term of the arithmetic sequence 4, 14, 24, 34, ...
244
First term a = 4 and common difference d = 10. Using a + (n − 1)d gives 4 + 24 × 10 = 244.
9. Find the 17th term of the arithmetic sequence 17, 21, 25, 29, ...
81
First term a = 17 and common difference d = 4. Using a + (n − 1)d gives 17 + 16 × 4 = 81.
10. Find the 17th term of the arithmetic sequence 10, 22, 34, 46, ...
202
First term a = 10 and common difference d = 12. Using a + (n − 1)d gives 10 + 16 × 12 = 202.
11. Find the 14th term of the arithmetic sequence 11, 20, 29, 38, ...
128
First term a = 11 and common difference d = 9. Using a + (n − 1)d gives 11 + 13 × 9 = 128.
12. Find the 8th term of the arithmetic sequence 6, 16, 26, 36, ...
76
First term a = 6 and common difference d = 10. Using a + (n − 1)d gives 6 + 7 × 10 = 76.

12 questions · Seed 104741 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Linear nth-term sequences

Take your time. Show your thinking.

1. Find the 19th term of the arithmetic sequence 10, 17, 24, 31, ...
2. Find the 14th term of the arithmetic sequence 10, 22, 34, 46, ...
3. Find the 16th term of the arithmetic sequence 13, 22, 31, 40, ...
4. Find the 16th term of the arithmetic sequence 15, 19, 23, 27, ...
5. Find the 16th term of the arithmetic sequence 23, 29, 35, 41, ...
6. Find the 16th term of the arithmetic sequence 22, 25, 28, 31, ...
7. Find the 25th term of the arithmetic sequence 14, 22, 30, 38, ...
8. Find the 25th term of the arithmetic sequence 4, 14, 24, 34, ...
9. Find the 17th term of the arithmetic sequence 17, 21, 25, 29, ...
10. Find the 17th term of the arithmetic sequence 10, 22, 34, 46, ...
11. Find the 14th term of the arithmetic sequence 11, 20, 29, 38, ...
12. Find the 8th term of the arithmetic sequence 6, 16, 26, 36, ...

12 questions · Seed 104741 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Linear nth-term sequences

Answers and reasoning. Review before teaching.

1. Find the 19th term of the arithmetic sequence 10, 17, 24, 31, ...
136
First term a = 10 and common difference d = 7. Using a + (n − 1)d gives 10 + 18 × 7 = 136.
2. Find the 14th term of the arithmetic sequence 10, 22, 34, 46, ...
166
First term a = 10 and common difference d = 12. Using a + (n − 1)d gives 10 + 13 × 12 = 166.
3. Find the 16th term of the arithmetic sequence 13, 22, 31, 40, ...
148
First term a = 13 and common difference d = 9. Using a + (n − 1)d gives 13 + 15 × 9 = 148.
4. Find the 16th term of the arithmetic sequence 15, 19, 23, 27, ...
75
First term a = 15 and common difference d = 4. Using a + (n − 1)d gives 15 + 15 × 4 = 75.
5. Find the 16th term of the arithmetic sequence 23, 29, 35, 41, ...
113
First term a = 23 and common difference d = 6. Using a + (n − 1)d gives 23 + 15 × 6 = 113.
6. Find the 16th term of the arithmetic sequence 22, 25, 28, 31, ...
67
First term a = 22 and common difference d = 3. Using a + (n − 1)d gives 22 + 15 × 3 = 67.
7. Find the 25th term of the arithmetic sequence 14, 22, 30, 38, ...
206
First term a = 14 and common difference d = 8. Using a + (n − 1)d gives 14 + 24 × 8 = 206.
8. Find the 25th term of the arithmetic sequence 4, 14, 24, 34, ...
244
First term a = 4 and common difference d = 10. Using a + (n − 1)d gives 4 + 24 × 10 = 244.
9. Find the 17th term of the arithmetic sequence 17, 21, 25, 29, ...
81
First term a = 17 and common difference d = 4. Using a + (n − 1)d gives 17 + 16 × 4 = 81.
10. Find the 17th term of the arithmetic sequence 10, 22, 34, 46, ...
202
First term a = 10 and common difference d = 12. Using a + (n − 1)d gives 10 + 16 × 12 = 202.
11. Find the 14th term of the arithmetic sequence 11, 20, 29, 38, ...
128
First term a = 11 and common difference d = 9. Using a + (n − 1)d gives 11 + 13 × 9 = 128.
12. Find the 8th term of the arithmetic sequence 6, 16, 26, 36, ...
76
First term a = 6 and common difference d = 10. Using a + (n − 1)d gives 6 + 7 × 10 = 76.

12 questions · Seed 104741 · Age guidance, not curriculum certification