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, 10, 20, 34, ____
2. Find the 5th term of the quadratic sequence: 11, 14, 19, 26, ____
3. Find the 5th term of the quadratic sequence: 2, 8, 18, 32, ____
4. Find the 5th term of the quadratic sequence: 16, 25, 40, 61, ____
5. Find the 5th term of the quadratic sequence: 10, 16, 26, 40, ____
6. Find the 5th term of the quadratic sequence: 15, 18, 23, 30, ____
7. Find the 5th term of the quadratic sequence: 18, 27, 42, 63, ____
8. Find the 5th term of the quadratic sequence: 15, 30, 55, 90, ____
9. Find the 5th term of the quadratic sequence: 17, 29, 49, 77, ____
10. Find the 5th term of the quadratic sequence: 8, 23, 48, 83, ____
11. Find the 5th term of the quadratic sequence: 8, 20, 40, 68, ____
12. Find the 5th term of the quadratic sequence: 4, 16, 36, 64, ____

12 questions · Seed 51 · 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, 10, 20, 34, ____
52
The nth term is 2n² + 2. For n = 5, 2 × 25 + 2 = 52.
2. Find the 5th term of the quadratic sequence: 11, 14, 19, 26, ____
35
The nth term is 1n² + 10. For n = 5, 1 × 25 + 10 = 35.
3. Find the 5th term of the quadratic sequence: 2, 8, 18, 32, ____
50
The nth term is 2n² + 0. For n = 5, 2 × 25 + 0 = 50.
4. Find the 5th term of the quadratic sequence: 16, 25, 40, 61, ____
88
The nth term is 3n² + 13. For n = 5, 3 × 25 + 13 = 88.
5. Find the 5th term of the quadratic sequence: 10, 16, 26, 40, ____
58
The nth term is 2n² + 8. For n = 5, 2 × 25 + 8 = 58.
6. 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.
7. Find the 5th term of the quadratic sequence: 18, 27, 42, 63, ____
90
The nth term is 3n² + 15. For n = 5, 3 × 25 + 15 = 90.
8. Find the 5th term of the quadratic sequence: 15, 30, 55, 90, ____
135
The nth term is 5n² + 10. For n = 5, 5 × 25 + 10 = 135.
9. 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.
10. Find the 5th term of the quadratic sequence: 8, 23, 48, 83, ____
128
The nth term is 5n² + 3. For n = 5, 5 × 25 + 3 = 128.
11. Find the 5th term of the quadratic sequence: 8, 20, 40, 68, ____
104
The nth term is 4n² + 4. For n = 5, 4 × 25 + 4 = 104.
12. 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.

12 questions · Seed 51 · 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, 10, 20, 34, ____
2. Find the 5th term of the quadratic sequence: 11, 14, 19, 26, ____
3. Find the 5th term of the quadratic sequence: 2, 8, 18, 32, ____
4. Find the 5th term of the quadratic sequence: 16, 25, 40, 61, ____
5. Find the 5th term of the quadratic sequence: 10, 16, 26, 40, ____
6. Find the 5th term of the quadratic sequence: 15, 18, 23, 30, ____
7. Find the 5th term of the quadratic sequence: 18, 27, 42, 63, ____
8. Find the 5th term of the quadratic sequence: 15, 30, 55, 90, ____
9. Find the 5th term of the quadratic sequence: 17, 29, 49, 77, ____
10. Find the 5th term of the quadratic sequence: 8, 23, 48, 83, ____
11. Find the 5th term of the quadratic sequence: 8, 20, 40, 68, ____
12. Find the 5th term of the quadratic sequence: 4, 16, 36, 64, ____

12 questions · Seed 51 · 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, 10, 20, 34, ____
52
The nth term is 2n² + 2. For n = 5, 2 × 25 + 2 = 52.
2. Find the 5th term of the quadratic sequence: 11, 14, 19, 26, ____
35
The nth term is 1n² + 10. For n = 5, 1 × 25 + 10 = 35.
3. Find the 5th term of the quadratic sequence: 2, 8, 18, 32, ____
50
The nth term is 2n² + 0. For n = 5, 2 × 25 + 0 = 50.
4. Find the 5th term of the quadratic sequence: 16, 25, 40, 61, ____
88
The nth term is 3n² + 13. For n = 5, 3 × 25 + 13 = 88.
5. Find the 5th term of the quadratic sequence: 10, 16, 26, 40, ____
58
The nth term is 2n² + 8. For n = 5, 2 × 25 + 8 = 58.
6. 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.
7. Find the 5th term of the quadratic sequence: 18, 27, 42, 63, ____
90
The nth term is 3n² + 15. For n = 5, 3 × 25 + 15 = 90.
8. Find the 5th term of the quadratic sequence: 15, 30, 55, 90, ____
135
The nth term is 5n² + 10. For n = 5, 5 × 25 + 10 = 135.
9. 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.
10. Find the 5th term of the quadratic sequence: 8, 23, 48, 83, ____
128
The nth term is 5n² + 3. For n = 5, 5 × 25 + 3 = 128.
11. Find the 5th term of the quadratic sequence: 8, 20, 40, 68, ____
104
The nth term is 4n² + 4. For n = 5, 4 × 25 + 4 = 104.
12. 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.

12 questions · Seed 51 · Age guidance, not curriculum certification