ReasoningAges 13-15

Second-difference sequences

Use first and second differences to find the next term in a quadratic number 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

Second-difference sequences

Take your time. Show your thinking.

1. Find the 5th term of the quadratic sequence: 17, 26, 41, 62, ____
2. Find the 5th term of the quadratic sequence: 4, 13, 28, 49, ____
3. Find the 5th term of the quadratic sequence: 16, 31, 56, 91, ____
4. Find the 5th term of the quadratic sequence: 6, 15, 30, 51, ____
5. Find the 5th term of the quadratic sequence: 15, 18, 23, 30, ____
6. Find the 5th term of the quadratic sequence: 13, 28, 53, 88, ____
7. Find the 5th term of the quadratic sequence: 17, 29, 49, 77, ____
8. Find the 5th term of the quadratic sequence: 7, 22, 47, 82, ____
9. Find the 5th term of the quadratic sequence: 1, 4, 9, 16, ____
10. Find the 5th term of the quadratic sequence: 19, 31, 51, 79, ____
11. Find the 5th term of the quadratic sequence: 10, 22, 42, 70, ____
12. Find the 5th term of the quadratic sequence: 14, 23, 38, 59, ____

12 questions · Seed 49 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 13-15

Second-difference sequences

Answers and reasoning. Review before teaching.

1. Find the 5th term of the quadratic sequence: 17, 26, 41, 62, ____
89
The nth term is 3n² + 14. For n = 5, 3 × 25 + 14 = 89.
2. Find the 5th term of the quadratic sequence: 4, 13, 28, 49, ____
76
The nth term is 3n² + 1. For n = 5, 3 × 25 + 1 = 76.
3. Find the 5th term of the quadratic sequence: 16, 31, 56, 91, ____
136
The nth term is 5n² + 11. For n = 5, 5 × 25 + 11 = 136.
4. Find the 5th term of the quadratic sequence: 6, 15, 30, 51, ____
78
The nth term is 3n² + 3. For n = 5, 3 × 25 + 3 = 78.
5. Find the 5th term of the quadratic sequence: 15, 18, 23, 30, ____
39
The nth term is 1n² + 14. For n = 5, 1 × 25 + 14 = 39.
6. Find the 5th term of the quadratic sequence: 13, 28, 53, 88, ____
133
The nth term is 5n² + 8. For n = 5, 5 × 25 + 8 = 133.
7. Find the 5th term of the quadratic sequence: 17, 29, 49, 77, ____
113
The nth term is 4n² + 13. For n = 5, 4 × 25 + 13 = 113.
8. Find the 5th term of the quadratic sequence: 7, 22, 47, 82, ____
127
The nth term is 5n² + 2. For n = 5, 5 × 25 + 2 = 127.
9. Find the 5th term of the quadratic sequence: 1, 4, 9, 16, ____
25
The nth term is 1n² + 0. For n = 5, 1 × 25 + 0 = 25.
10. Find the 5th term of the quadratic sequence: 19, 31, 51, 79, ____
115
The nth term is 4n² + 15. For n = 5, 4 × 25 + 15 = 115.
11. Find the 5th term of the quadratic sequence: 10, 22, 42, 70, ____
106
The nth term is 4n² + 6. For n = 5, 4 × 25 + 6 = 106.
12. Find the 5th term of the quadratic sequence: 14, 23, 38, 59, ____
86
The nth term is 3n² + 11. For n = 5, 3 × 25 + 11 = 86.

12 questions · Seed 49 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Second-difference sequences

Take your time. Show your thinking.

1. Find the 5th term of the quadratic sequence: 17, 26, 41, 62, ____
2. Find the 5th term of the quadratic sequence: 4, 13, 28, 49, ____
3. Find the 5th term of the quadratic sequence: 16, 31, 56, 91, ____
4. Find the 5th term of the quadratic sequence: 6, 15, 30, 51, ____
5. Find the 5th term of the quadratic sequence: 15, 18, 23, 30, ____
6. Find the 5th term of the quadratic sequence: 13, 28, 53, 88, ____
7. Find the 5th term of the quadratic sequence: 17, 29, 49, 77, ____
8. Find the 5th term of the quadratic sequence: 7, 22, 47, 82, ____
9. Find the 5th term of the quadratic sequence: 1, 4, 9, 16, ____
10. Find the 5th term of the quadratic sequence: 19, 31, 51, 79, ____
11. Find the 5th term of the quadratic sequence: 10, 22, 42, 70, ____
12. Find the 5th term of the quadratic sequence: 14, 23, 38, 59, ____

12 questions · Seed 49 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Second-difference sequences

Answers and reasoning. Review before teaching.

1. Find the 5th term of the quadratic sequence: 17, 26, 41, 62, ____
89
The nth term is 3n² + 14. For n = 5, 3 × 25 + 14 = 89.
2. Find the 5th term of the quadratic sequence: 4, 13, 28, 49, ____
76
The nth term is 3n² + 1. For n = 5, 3 × 25 + 1 = 76.
3. Find the 5th term of the quadratic sequence: 16, 31, 56, 91, ____
136
The nth term is 5n² + 11. For n = 5, 5 × 25 + 11 = 136.
4. Find the 5th term of the quadratic sequence: 6, 15, 30, 51, ____
78
The nth term is 3n² + 3. For n = 5, 3 × 25 + 3 = 78.
5. Find the 5th term of the quadratic sequence: 15, 18, 23, 30, ____
39
The nth term is 1n² + 14. For n = 5, 1 × 25 + 14 = 39.
6. Find the 5th term of the quadratic sequence: 13, 28, 53, 88, ____
133
The nth term is 5n² + 8. For n = 5, 5 × 25 + 8 = 133.
7. Find the 5th term of the quadratic sequence: 17, 29, 49, 77, ____
113
The nth term is 4n² + 13. For n = 5, 4 × 25 + 13 = 113.
8. Find the 5th term of the quadratic sequence: 7, 22, 47, 82, ____
127
The nth term is 5n² + 2. For n = 5, 5 × 25 + 2 = 127.
9. Find the 5th term of the quadratic sequence: 1, 4, 9, 16, ____
25
The nth term is 1n² + 0. For n = 5, 1 × 25 + 0 = 25.
10. Find the 5th term of the quadratic sequence: 19, 31, 51, 79, ____
115
The nth term is 4n² + 15. For n = 5, 4 × 25 + 15 = 115.
11. Find the 5th term of the quadratic sequence: 10, 22, 42, 70, ____
106
The nth term is 4n² + 6. For n = 5, 4 × 25 + 6 = 106.
12. Find the 5th term of the quadratic sequence: 14, 23, 38, 59, ____
86
The nth term is 3n² + 11. For n = 5, 3 × 25 + 11 = 86.

12 questions · Seed 49 · Age guidance, not curriculum certification