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 11th term of the arithmetic sequence 19, 31, 43, 55, ...
2. Find the 10th term of the arithmetic sequence 15, 27, 39, 51, ...
3. Find the 19th term of the arithmetic sequence 12, 21, 30, 39, ...
4. Find the 15th term of the arithmetic sequence 4, 13, 22, 31, ...
5. Find the 17th term of the arithmetic sequence 5, 8, 11, 14, ...
6. Find the 24th term of the arithmetic sequence 19, 27, 35, 43, ...
7. Find the 18th term of the arithmetic sequence 6, 9, 12, 15, ...
8. Find the 17th term of the arithmetic sequence 14, 18, 22, 26, ...
9. Find the 8th term of the arithmetic sequence 16, 28, 40, 52, ...
10. Find the 23th term of the arithmetic sequence 23, 33, 43, 53, ...
11. Find the 16th term of the arithmetic sequence 6, 11, 16, 21, ...
12. Find the 15th term of the arithmetic sequence 7, 11, 15, 19, ...

12 questions · Seed 104736 · 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 11th term of the arithmetic sequence 19, 31, 43, 55, ...
139
First term a = 19 and common difference d = 12. Using a + (n − 1)d gives 19 + 10 × 12 = 139.
2. Find the 10th term of the arithmetic sequence 15, 27, 39, 51, ...
123
First term a = 15 and common difference d = 12. Using a + (n − 1)d gives 15 + 9 × 12 = 123.
3. Find the 19th term of the arithmetic sequence 12, 21, 30, 39, ...
174
First term a = 12 and common difference d = 9. Using a + (n − 1)d gives 12 + 18 × 9 = 174.
4. Find the 15th term of the arithmetic sequence 4, 13, 22, 31, ...
130
First term a = 4 and common difference d = 9. Using a + (n − 1)d gives 4 + 14 × 9 = 130.
5. Find the 17th term of the arithmetic sequence 5, 8, 11, 14, ...
53
First term a = 5 and common difference d = 3. Using a + (n − 1)d gives 5 + 16 × 3 = 53.
6. Find the 24th term of the arithmetic sequence 19, 27, 35, 43, ...
203
First term a = 19 and common difference d = 8. Using a + (n − 1)d gives 19 + 23 × 8 = 203.
7. Find the 18th term of the arithmetic sequence 6, 9, 12, 15, ...
57
First term a = 6 and common difference d = 3. Using a + (n − 1)d gives 6 + 17 × 3 = 57.
8. Find the 17th term of the arithmetic sequence 14, 18, 22, 26, ...
78
First term a = 14 and common difference d = 4. Using a + (n − 1)d gives 14 + 16 × 4 = 78.
9. Find the 8th term of the arithmetic sequence 16, 28, 40, 52, ...
100
First term a = 16 and common difference d = 12. Using a + (n − 1)d gives 16 + 7 × 12 = 100.
10. Find the 23th term of the arithmetic sequence 23, 33, 43, 53, ...
243
First term a = 23 and common difference d = 10. Using a + (n − 1)d gives 23 + 22 × 10 = 243.
11. Find the 16th term of the arithmetic sequence 6, 11, 16, 21, ...
81
First term a = 6 and common difference d = 5. Using a + (n − 1)d gives 6 + 15 × 5 = 81.
12. Find the 15th term of the arithmetic sequence 7, 11, 15, 19, ...
63
First term a = 7 and common difference d = 4. Using a + (n − 1)d gives 7 + 14 × 4 = 63.

12 questions · Seed 104736 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Linear nth-term sequences

Take your time. Show your thinking.

1. Find the 11th term of the arithmetic sequence 19, 31, 43, 55, ...
2. Find the 10th term of the arithmetic sequence 15, 27, 39, 51, ...
3. Find the 19th term of the arithmetic sequence 12, 21, 30, 39, ...
4. Find the 15th term of the arithmetic sequence 4, 13, 22, 31, ...
5. Find the 17th term of the arithmetic sequence 5, 8, 11, 14, ...
6. Find the 24th term of the arithmetic sequence 19, 27, 35, 43, ...
7. Find the 18th term of the arithmetic sequence 6, 9, 12, 15, ...
8. Find the 17th term of the arithmetic sequence 14, 18, 22, 26, ...
9. Find the 8th term of the arithmetic sequence 16, 28, 40, 52, ...
10. Find the 23th term of the arithmetic sequence 23, 33, 43, 53, ...
11. Find the 16th term of the arithmetic sequence 6, 11, 16, 21, ...
12. Find the 15th term of the arithmetic sequence 7, 11, 15, 19, ...

12 questions · Seed 104736 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Linear nth-term sequences

Answers and reasoning. Review before teaching.

1. Find the 11th term of the arithmetic sequence 19, 31, 43, 55, ...
139
First term a = 19 and common difference d = 12. Using a + (n − 1)d gives 19 + 10 × 12 = 139.
2. Find the 10th term of the arithmetic sequence 15, 27, 39, 51, ...
123
First term a = 15 and common difference d = 12. Using a + (n − 1)d gives 15 + 9 × 12 = 123.
3. Find the 19th term of the arithmetic sequence 12, 21, 30, 39, ...
174
First term a = 12 and common difference d = 9. Using a + (n − 1)d gives 12 + 18 × 9 = 174.
4. Find the 15th term of the arithmetic sequence 4, 13, 22, 31, ...
130
First term a = 4 and common difference d = 9. Using a + (n − 1)d gives 4 + 14 × 9 = 130.
5. Find the 17th term of the arithmetic sequence 5, 8, 11, 14, ...
53
First term a = 5 and common difference d = 3. Using a + (n − 1)d gives 5 + 16 × 3 = 53.
6. Find the 24th term of the arithmetic sequence 19, 27, 35, 43, ...
203
First term a = 19 and common difference d = 8. Using a + (n − 1)d gives 19 + 23 × 8 = 203.
7. Find the 18th term of the arithmetic sequence 6, 9, 12, 15, ...
57
First term a = 6 and common difference d = 3. Using a + (n − 1)d gives 6 + 17 × 3 = 57.
8. Find the 17th term of the arithmetic sequence 14, 18, 22, 26, ...
78
First term a = 14 and common difference d = 4. Using a + (n − 1)d gives 14 + 16 × 4 = 78.
9. Find the 8th term of the arithmetic sequence 16, 28, 40, 52, ...
100
First term a = 16 and common difference d = 12. Using a + (n − 1)d gives 16 + 7 × 12 = 100.
10. Find the 23th term of the arithmetic sequence 23, 33, 43, 53, ...
243
First term a = 23 and common difference d = 10. Using a + (n − 1)d gives 23 + 22 × 10 = 243.
11. Find the 16th term of the arithmetic sequence 6, 11, 16, 21, ...
81
First term a = 6 and common difference d = 5. Using a + (n − 1)d gives 6 + 15 × 5 = 81.
12. Find the 15th term of the arithmetic sequence 7, 11, 15, 19, ...
63
First term a = 7 and common difference d = 4. Using a + (n − 1)d gives 7 + 14 × 4 = 63.

12 questions · Seed 104736 · Age guidance, not curriculum certification