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 23th term of the arithmetic sequence 21, 28, 35, 42, ...
2. Find the 15th term of the arithmetic sequence 17, 28, 39, 50, ...
3. Find the 14th term of the arithmetic sequence 14, 19, 24, 29, ...
4. Find the 17th term of the arithmetic sequence 21, 29, 37, 45, ...
5. Find the 13th term of the arithmetic sequence 23, 31, 39, 47, ...
6. Find the 14th term of the arithmetic sequence 18, 29, 40, 51, ...
7. Find the 16th term of the arithmetic sequence 24, 31, 38, 45, ...
8. Find the 20th term of the arithmetic sequence 13, 23, 33, 43, ...
9. Find the 12th term of the arithmetic sequence 19, 26, 33, 40, ...
10. Find the 14th term of the arithmetic sequence 10, 15, 20, 25, ...
11. Find the 14th term of the arithmetic sequence 9, 19, 29, 39, ...
12. Find the 12th term of the arithmetic sequence 9, 17, 25, 33, ...

12 questions · Seed 52 · 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 23th term of the arithmetic sequence 21, 28, 35, 42, ...
175
First term a = 21 and common difference d = 7. Using a + (n − 1)d gives 21 + 22 × 7 = 175.
2. Find the 15th term of the arithmetic sequence 17, 28, 39, 50, ...
171
First term a = 17 and common difference d = 11. Using a + (n − 1)d gives 17 + 14 × 11 = 171.
3. Find the 14th term of the arithmetic sequence 14, 19, 24, 29, ...
79
First term a = 14 and common difference d = 5. Using a + (n − 1)d gives 14 + 13 × 5 = 79.
4. Find the 17th term of the arithmetic sequence 21, 29, 37, 45, ...
149
First term a = 21 and common difference d = 8. Using a + (n − 1)d gives 21 + 16 × 8 = 149.
5. Find the 13th term of the arithmetic sequence 23, 31, 39, 47, ...
119
First term a = 23 and common difference d = 8. Using a + (n − 1)d gives 23 + 12 × 8 = 119.
6. Find the 14th term of the arithmetic sequence 18, 29, 40, 51, ...
161
First term a = 18 and common difference d = 11. Using a + (n − 1)d gives 18 + 13 × 11 = 161.
7. Find the 16th term of the arithmetic sequence 24, 31, 38, 45, ...
129
First term a = 24 and common difference d = 7. Using a + (n − 1)d gives 24 + 15 × 7 = 129.
8. Find the 20th term of the arithmetic sequence 13, 23, 33, 43, ...
203
First term a = 13 and common difference d = 10. Using a + (n − 1)d gives 13 + 19 × 10 = 203.
9. Find the 12th term of the arithmetic sequence 19, 26, 33, 40, ...
96
First term a = 19 and common difference d = 7. Using a + (n − 1)d gives 19 + 11 × 7 = 96.
10. Find the 14th term of the arithmetic sequence 10, 15, 20, 25, ...
75
First term a = 10 and common difference d = 5. Using a + (n − 1)d gives 10 + 13 × 5 = 75.
11. Find the 14th term of the arithmetic sequence 9, 19, 29, 39, ...
139
First term a = 9 and common difference d = 10. Using a + (n − 1)d gives 9 + 13 × 10 = 139.
12. Find the 12th term of the arithmetic sequence 9, 17, 25, 33, ...
97
First term a = 9 and common difference d = 8. Using a + (n − 1)d gives 9 + 11 × 8 = 97.

12 questions · Seed 52 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Linear nth-term sequences

Take your time. Show your thinking.

1. Find the 23th term of the arithmetic sequence 21, 28, 35, 42, ...
2. Find the 15th term of the arithmetic sequence 17, 28, 39, 50, ...
3. Find the 14th term of the arithmetic sequence 14, 19, 24, 29, ...
4. Find the 17th term of the arithmetic sequence 21, 29, 37, 45, ...
5. Find the 13th term of the arithmetic sequence 23, 31, 39, 47, ...
6. Find the 14th term of the arithmetic sequence 18, 29, 40, 51, ...
7. Find the 16th term of the arithmetic sequence 24, 31, 38, 45, ...
8. Find the 20th term of the arithmetic sequence 13, 23, 33, 43, ...
9. Find the 12th term of the arithmetic sequence 19, 26, 33, 40, ...
10. Find the 14th term of the arithmetic sequence 10, 15, 20, 25, ...
11. Find the 14th term of the arithmetic sequence 9, 19, 29, 39, ...
12. Find the 12th term of the arithmetic sequence 9, 17, 25, 33, ...

12 questions · Seed 52 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Linear nth-term sequences

Answers and reasoning. Review before teaching.

1. Find the 23th term of the arithmetic sequence 21, 28, 35, 42, ...
175
First term a = 21 and common difference d = 7. Using a + (n − 1)d gives 21 + 22 × 7 = 175.
2. Find the 15th term of the arithmetic sequence 17, 28, 39, 50, ...
171
First term a = 17 and common difference d = 11. Using a + (n − 1)d gives 17 + 14 × 11 = 171.
3. Find the 14th term of the arithmetic sequence 14, 19, 24, 29, ...
79
First term a = 14 and common difference d = 5. Using a + (n − 1)d gives 14 + 13 × 5 = 79.
4. Find the 17th term of the arithmetic sequence 21, 29, 37, 45, ...
149
First term a = 21 and common difference d = 8. Using a + (n − 1)d gives 21 + 16 × 8 = 149.
5. Find the 13th term of the arithmetic sequence 23, 31, 39, 47, ...
119
First term a = 23 and common difference d = 8. Using a + (n − 1)d gives 23 + 12 × 8 = 119.
6. Find the 14th term of the arithmetic sequence 18, 29, 40, 51, ...
161
First term a = 18 and common difference d = 11. Using a + (n − 1)d gives 18 + 13 × 11 = 161.
7. Find the 16th term of the arithmetic sequence 24, 31, 38, 45, ...
129
First term a = 24 and common difference d = 7. Using a + (n − 1)d gives 24 + 15 × 7 = 129.
8. Find the 20th term of the arithmetic sequence 13, 23, 33, 43, ...
203
First term a = 13 and common difference d = 10. Using a + (n − 1)d gives 13 + 19 × 10 = 203.
9. Find the 12th term of the arithmetic sequence 19, 26, 33, 40, ...
96
First term a = 19 and common difference d = 7. Using a + (n − 1)d gives 19 + 11 × 7 = 96.
10. Find the 14th term of the arithmetic sequence 10, 15, 20, 25, ...
75
First term a = 10 and common difference d = 5. Using a + (n − 1)d gives 10 + 13 × 5 = 75.
11. Find the 14th term of the arithmetic sequence 9, 19, 29, 39, ...
139
First term a = 9 and common difference d = 10. Using a + (n − 1)d gives 9 + 13 × 10 = 139.
12. Find the 12th term of the arithmetic sequence 9, 17, 25, 33, ...
97
First term a = 9 and common difference d = 8. Using a + (n − 1)d gives 9 + 11 × 8 = 97.

12 questions · Seed 52 · Age guidance, not curriculum certification