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: 13, 19, 29, 43, ____
2. Find the 5th term of the quadratic sequence: 9, 18, 33, 54, ____
3. Find the 5th term of the quadratic sequence: 15, 27, 47, 75, ____
4. Find the 5th term of the quadratic sequence: 18, 33, 58, 93, ____
5. Find the 5th term of the quadratic sequence: 14, 17, 22, 29, ____
6. Find the 5th term of the quadratic sequence: 13, 25, 45, 73, ____
7. Find the 5th term of the quadratic sequence: 10, 22, 42, 70, ____
8. Find the 5th term of the quadratic sequence: 12, 27, 52, 87, ____
9. Find the 5th term of the quadratic sequence: 13, 28, 53, 88, ____
10. Find the 5th term of the quadratic sequence: 17, 26, 41, 62, ____
11. Find the 5th term of the quadratic sequence: 14, 23, 38, 59, ____
12. Find the 5th term of the quadratic sequence: 8, 11, 16, 23, ____

12 questions · Seed 47 · 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: 13, 19, 29, 43, ____
61
The nth term is 2n² + 11. For n = 5, 2 × 25 + 11 = 61.
2. Find the 5th term of the quadratic sequence: 9, 18, 33, 54, ____
81
The nth term is 3n² + 6. For n = 5, 3 × 25 + 6 = 81.
3. Find the 5th term of the quadratic sequence: 15, 27, 47, 75, ____
111
The nth term is 4n² + 11. For n = 5, 4 × 25 + 11 = 111.
4. Find the 5th term of the quadratic sequence: 18, 33, 58, 93, ____
138
The nth term is 5n² + 13. For n = 5, 5 × 25 + 13 = 138.
5. 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.
6. Find the 5th term of the quadratic sequence: 13, 25, 45, 73, ____
109
The nth term is 4n² + 9. For n = 5, 4 × 25 + 9 = 109.
7. 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.
8. Find the 5th term of the quadratic sequence: 12, 27, 52, 87, ____
132
The nth term is 5n² + 7. For n = 5, 5 × 25 + 7 = 132.
9. 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.
10. 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.
11. 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. 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.

12 questions · Seed 47 · 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: 13, 19, 29, 43, ____
2. Find the 5th term of the quadratic sequence: 9, 18, 33, 54, ____
3. Find the 5th term of the quadratic sequence: 15, 27, 47, 75, ____
4. Find the 5th term of the quadratic sequence: 18, 33, 58, 93, ____
5. Find the 5th term of the quadratic sequence: 14, 17, 22, 29, ____
6. Find the 5th term of the quadratic sequence: 13, 25, 45, 73, ____
7. Find the 5th term of the quadratic sequence: 10, 22, 42, 70, ____
8. Find the 5th term of the quadratic sequence: 12, 27, 52, 87, ____
9. Find the 5th term of the quadratic sequence: 13, 28, 53, 88, ____
10. Find the 5th term of the quadratic sequence: 17, 26, 41, 62, ____
11. Find the 5th term of the quadratic sequence: 14, 23, 38, 59, ____
12. Find the 5th term of the quadratic sequence: 8, 11, 16, 23, ____

12 questions · Seed 47 · 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: 13, 19, 29, 43, ____
61
The nth term is 2n² + 11. For n = 5, 2 × 25 + 11 = 61.
2. Find the 5th term of the quadratic sequence: 9, 18, 33, 54, ____
81
The nth term is 3n² + 6. For n = 5, 3 × 25 + 6 = 81.
3. Find the 5th term of the quadratic sequence: 15, 27, 47, 75, ____
111
The nth term is 4n² + 11. For n = 5, 4 × 25 + 11 = 111.
4. Find the 5th term of the quadratic sequence: 18, 33, 58, 93, ____
138
The nth term is 5n² + 13. For n = 5, 5 × 25 + 13 = 138.
5. 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.
6. Find the 5th term of the quadratic sequence: 13, 25, 45, 73, ____
109
The nth term is 4n² + 9. For n = 5, 4 × 25 + 9 = 109.
7. 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.
8. Find the 5th term of the quadratic sequence: 12, 27, 52, 87, ____
132
The nth term is 5n² + 7. For n = 5, 5 × 25 + 7 = 132.
9. 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.
10. 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.
11. 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. 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.

12 questions · Seed 47 · Age guidance, not curriculum certification