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: 4, 16, 36, 64, ____
2. Find the 5th term of the quadratic sequence: 16, 22, 32, 46, ____
3. Find the 5th term of the quadratic sequence: 5, 8, 13, 20, ____
4. Find the 5th term of the quadratic sequence: 12, 21, 36, 57, ____
5. Find the 5th term of the quadratic sequence: 20, 35, 60, 95, ____
6. Find the 5th term of the quadratic sequence: 6, 21, 46, 81, ____
7. Find the 5th term of the quadratic sequence: 12, 15, 20, 27, ____
8. Find the 5th term of the quadratic sequence: 7, 22, 47, 82, ____
9. Find the 5th term of the quadratic sequence: 8, 11, 16, 23, ____
10. Find the 5th term of the quadratic sequence: 4, 13, 28, 49, ____
11. Find the 5th term of the quadratic sequence: 14, 29, 54, 89, ____
12. Find the 5th term of the quadratic sequence: 14, 17, 22, 29, ____

12 questions · Seed 54 · 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: 4, 16, 36, 64, ____
100
The nth term is 4n² + 0. For n = 5, 4 × 25 + 0 = 100.
2. Find the 5th term of the quadratic sequence: 16, 22, 32, 46, ____
64
The nth term is 2n² + 14. For n = 5, 2 × 25 + 14 = 64.
3. Find the 5th term of the quadratic sequence: 5, 8, 13, 20, ____
29
The nth term is 1n² + 4. For n = 5, 1 × 25 + 4 = 29.
4. Find the 5th term of the quadratic sequence: 12, 21, 36, 57, ____
84
The nth term is 3n² + 9. For n = 5, 3 × 25 + 9 = 84.
5. Find the 5th term of the quadratic sequence: 20, 35, 60, 95, ____
140
The nth term is 5n² + 15. For n = 5, 5 × 25 + 15 = 140.
6. Find the 5th term of the quadratic sequence: 6, 21, 46, 81, ____
126
The nth term is 5n² + 1. For n = 5, 5 × 25 + 1 = 126.
7. Find the 5th term of the quadratic sequence: 12, 15, 20, 27, ____
36
The nth term is 1n² + 11. For n = 5, 1 × 25 + 11 = 36.
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: 8, 11, 16, 23, ____
32
The nth term is 1n² + 7. For n = 5, 1 × 25 + 7 = 32.
10. 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.
11. Find the 5th term of the quadratic sequence: 14, 29, 54, 89, ____
134
The nth term is 5n² + 9. For n = 5, 5 × 25 + 9 = 134.
12. Find the 5th term of the quadratic sequence: 14, 17, 22, 29, ____
38
The nth term is 1n² + 13. For n = 5, 1 × 25 + 13 = 38.

12 questions · Seed 54 · 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: 4, 16, 36, 64, ____
2. Find the 5th term of the quadratic sequence: 16, 22, 32, 46, ____
3. Find the 5th term of the quadratic sequence: 5, 8, 13, 20, ____
4. Find the 5th term of the quadratic sequence: 12, 21, 36, 57, ____
5. Find the 5th term of the quadratic sequence: 20, 35, 60, 95, ____
6. Find the 5th term of the quadratic sequence: 6, 21, 46, 81, ____
7. Find the 5th term of the quadratic sequence: 12, 15, 20, 27, ____
8. Find the 5th term of the quadratic sequence: 7, 22, 47, 82, ____
9. Find the 5th term of the quadratic sequence: 8, 11, 16, 23, ____
10. Find the 5th term of the quadratic sequence: 4, 13, 28, 49, ____
11. Find the 5th term of the quadratic sequence: 14, 29, 54, 89, ____
12. Find the 5th term of the quadratic sequence: 14, 17, 22, 29, ____

12 questions · Seed 54 · 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: 4, 16, 36, 64, ____
100
The nth term is 4n² + 0. For n = 5, 4 × 25 + 0 = 100.
2. Find the 5th term of the quadratic sequence: 16, 22, 32, 46, ____
64
The nth term is 2n² + 14. For n = 5, 2 × 25 + 14 = 64.
3. Find the 5th term of the quadratic sequence: 5, 8, 13, 20, ____
29
The nth term is 1n² + 4. For n = 5, 1 × 25 + 4 = 29.
4. Find the 5th term of the quadratic sequence: 12, 21, 36, 57, ____
84
The nth term is 3n² + 9. For n = 5, 3 × 25 + 9 = 84.
5. Find the 5th term of the quadratic sequence: 20, 35, 60, 95, ____
140
The nth term is 5n² + 15. For n = 5, 5 × 25 + 15 = 140.
6. Find the 5th term of the quadratic sequence: 6, 21, 46, 81, ____
126
The nth term is 5n² + 1. For n = 5, 5 × 25 + 1 = 126.
7. Find the 5th term of the quadratic sequence: 12, 15, 20, 27, ____
36
The nth term is 1n² + 11. For n = 5, 1 × 25 + 11 = 36.
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: 8, 11, 16, 23, ____
32
The nth term is 1n² + 7. For n = 5, 1 × 25 + 7 = 32.
10. 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.
11. Find the 5th term of the quadratic sequence: 14, 29, 54, 89, ____
134
The nth term is 5n² + 9. For n = 5, 5 × 25 + 9 = 134.
12. Find the 5th term of the quadratic sequence: 14, 17, 22, 29, ____
38
The nth term is 1n² + 13. For n = 5, 1 × 25 + 13 = 38.

12 questions · Seed 54 · Age guidance, not curriculum certification