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 22th term of the arithmetic sequence 9, 15, 21, 27, ...
2. Find the 21th term of the arithmetic sequence 18, 30, 42, 54, ...
3. Find the 20th term of the arithmetic sequence 5, 17, 29, 41, ...
4. Find the 12th term of the arithmetic sequence 4, 12, 20, 28, ...
5. Find the 25th term of the arithmetic sequence 19, 31, 43, 55, ...
6. Find the 11th term of the arithmetic sequence 25, 28, 31, 34, ...
7. Find the 8th term of the arithmetic sequence 15, 27, 39, 51, ...
8. Find the 17th term of the arithmetic sequence 17, 22, 27, 32, ...
9. Find the 22th term of the arithmetic sequence 18, 27, 36, 45, ...
10. Find the 25th term of the arithmetic sequence 4, 10, 16, 22, ...
11. Find the 16th term of the arithmetic sequence 21, 32, 43, 54, ...
12. Find the 18th term of the arithmetic sequence 7, 13, 19, 25, ...

12 questions · Seed 104729 · Age guidance, not curriculum certification

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Worksheet StudioAnswer key · Ages 13-15

Linear nth-term sequences

Answers and reasoning. Review before teaching.

1. Find the 22th term of the arithmetic sequence 9, 15, 21, 27, ...
135
First term a = 9 and common difference d = 6. Using a + (n − 1)d gives 9 + 21 × 6 = 135.
2. Find the 21th term of the arithmetic sequence 18, 30, 42, 54, ...
258
First term a = 18 and common difference d = 12. Using a + (n − 1)d gives 18 + 20 × 12 = 258.
3. Find the 20th term of the arithmetic sequence 5, 17, 29, 41, ...
233
First term a = 5 and common difference d = 12. Using a + (n − 1)d gives 5 + 19 × 12 = 233.
4. Find the 12th term of the arithmetic sequence 4, 12, 20, 28, ...
92
First term a = 4 and common difference d = 8. Using a + (n − 1)d gives 4 + 11 × 8 = 92.
5. Find the 25th term of the arithmetic sequence 19, 31, 43, 55, ...
307
First term a = 19 and common difference d = 12. Using a + (n − 1)d gives 19 + 24 × 12 = 307.
6. Find the 11th term of the arithmetic sequence 25, 28, 31, 34, ...
55
First term a = 25 and common difference d = 3. Using a + (n − 1)d gives 25 + 10 × 3 = 55.
7. Find the 8th term of the arithmetic sequence 15, 27, 39, 51, ...
99
First term a = 15 and common difference d = 12. Using a + (n − 1)d gives 15 + 7 × 12 = 99.
8. Find the 17th term of the arithmetic sequence 17, 22, 27, 32, ...
97
First term a = 17 and common difference d = 5. Using a + (n − 1)d gives 17 + 16 × 5 = 97.
9. Find the 22th term of the arithmetic sequence 18, 27, 36, 45, ...
207
First term a = 18 and common difference d = 9. Using a + (n − 1)d gives 18 + 21 × 9 = 207.
10. Find the 25th term of the arithmetic sequence 4, 10, 16, 22, ...
148
First term a = 4 and common difference d = 6. Using a + (n − 1)d gives 4 + 24 × 6 = 148.
11. Find the 16th term of the arithmetic sequence 21, 32, 43, 54, ...
186
First term a = 21 and common difference d = 11. Using a + (n − 1)d gives 21 + 15 × 11 = 186.
12. Find the 18th term of the arithmetic sequence 7, 13, 19, 25, ...
109
First term a = 7 and common difference d = 6. Using a + (n − 1)d gives 7 + 17 × 6 = 109.

12 questions · Seed 104729 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Linear nth-term sequences

Take your time. Show your thinking.

1. Find the 22th term of the arithmetic sequence 9, 15, 21, 27, ...
2. Find the 21th term of the arithmetic sequence 18, 30, 42, 54, ...
3. Find the 20th term of the arithmetic sequence 5, 17, 29, 41, ...
4. Find the 12th term of the arithmetic sequence 4, 12, 20, 28, ...
5. Find the 25th term of the arithmetic sequence 19, 31, 43, 55, ...
6. Find the 11th term of the arithmetic sequence 25, 28, 31, 34, ...
7. Find the 8th term of the arithmetic sequence 15, 27, 39, 51, ...
8. Find the 17th term of the arithmetic sequence 17, 22, 27, 32, ...
9. Find the 22th term of the arithmetic sequence 18, 27, 36, 45, ...
10. Find the 25th term of the arithmetic sequence 4, 10, 16, 22, ...
11. Find the 16th term of the arithmetic sequence 21, 32, 43, 54, ...
12. Find the 18th term of the arithmetic sequence 7, 13, 19, 25, ...

12 questions · Seed 104729 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Linear nth-term sequences

Answers and reasoning. Review before teaching.

1. Find the 22th term of the arithmetic sequence 9, 15, 21, 27, ...
135
First term a = 9 and common difference d = 6. Using a + (n − 1)d gives 9 + 21 × 6 = 135.
2. Find the 21th term of the arithmetic sequence 18, 30, 42, 54, ...
258
First term a = 18 and common difference d = 12. Using a + (n − 1)d gives 18 + 20 × 12 = 258.
3. Find the 20th term of the arithmetic sequence 5, 17, 29, 41, ...
233
First term a = 5 and common difference d = 12. Using a + (n − 1)d gives 5 + 19 × 12 = 233.
4. Find the 12th term of the arithmetic sequence 4, 12, 20, 28, ...
92
First term a = 4 and common difference d = 8. Using a + (n − 1)d gives 4 + 11 × 8 = 92.
5. Find the 25th term of the arithmetic sequence 19, 31, 43, 55, ...
307
First term a = 19 and common difference d = 12. Using a + (n − 1)d gives 19 + 24 × 12 = 307.
6. Find the 11th term of the arithmetic sequence 25, 28, 31, 34, ...
55
First term a = 25 and common difference d = 3. Using a + (n − 1)d gives 25 + 10 × 3 = 55.
7. Find the 8th term of the arithmetic sequence 15, 27, 39, 51, ...
99
First term a = 15 and common difference d = 12. Using a + (n − 1)d gives 15 + 7 × 12 = 99.
8. Find the 17th term of the arithmetic sequence 17, 22, 27, 32, ...
97
First term a = 17 and common difference d = 5. Using a + (n − 1)d gives 17 + 16 × 5 = 97.
9. Find the 22th term of the arithmetic sequence 18, 27, 36, 45, ...
207
First term a = 18 and common difference d = 9. Using a + (n − 1)d gives 18 + 21 × 9 = 207.
10. Find the 25th term of the arithmetic sequence 4, 10, 16, 22, ...
148
First term a = 4 and common difference d = 6. Using a + (n − 1)d gives 4 + 24 × 6 = 148.
11. Find the 16th term of the arithmetic sequence 21, 32, 43, 54, ...
186
First term a = 21 and common difference d = 11. Using a + (n − 1)d gives 21 + 15 × 11 = 186.
12. Find the 18th term of the arithmetic sequence 7, 13, 19, 25, ...
109
First term a = 7 and common difference d = 6. Using a + (n − 1)d gives 7 + 17 × 6 = 109.

12 questions · Seed 104729 · Age guidance, not curriculum certification