ReasoningAges 16-18

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 16-18

Second-difference sequences

Take your time. Show your thinking.

1. Find the 5th term of the quadratic sequence: 11, 23, 43, 71, ____
2. Find the 5th term of the quadratic sequence: 6, 12, 22, 36, ____
3. Find the 5th term of the quadratic sequence: 8, 17, 32, 53, ____
4. Find the 5th term of the quadratic sequence: 10, 13, 18, 25, ____
5. Find the 5th term of the quadratic sequence: 3, 6, 11, 18, ____
6. Find the 5th term of the quadratic sequence: 17, 29, 49, 77, ____
7. Find the 5th term of the quadratic sequence: 4, 10, 20, 34, ____
8. Find the 5th term of the quadratic sequence: 7, 10, 15, 22, ____
9. Find the 5th term of the quadratic sequence: 13, 28, 53, 88, ____
10. Find the 5th term of the quadratic sequence: 19, 34, 59, 94, ____
11. Find the 5th term of the quadratic sequence: 19, 31, 51, 79, ____
12. Find the 5th term of the quadratic sequence: 4, 7, 12, 19, ____

12 questions · Seed 104733 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 16-18

Second-difference sequences

Answers and reasoning. Review before teaching.

1. Find the 5th term of the quadratic sequence: 11, 23, 43, 71, ____
107
The nth term is 4n² + 7. For n = 5, 4 × 25 + 7 = 107.
2. Find the 5th term of the quadratic sequence: 6, 12, 22, 36, ____
54
The nth term is 2n² + 4. For n = 5, 2 × 25 + 4 = 54.
3. Find the 5th term of the quadratic sequence: 8, 17, 32, 53, ____
80
The nth term is 3n² + 5. For n = 5, 3 × 25 + 5 = 80.
4. Find the 5th term of the quadratic sequence: 10, 13, 18, 25, ____
34
The nth term is 1n² + 9. For n = 5, 1 × 25 + 9 = 34.
5. Find the 5th term of the quadratic sequence: 3, 6, 11, 18, ____
27
The nth term is 1n² + 2. For n = 5, 1 × 25 + 2 = 27.
6. 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.
7. 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.
8. Find the 5th term of the quadratic sequence: 7, 10, 15, 22, ____
31
The nth term is 1n² + 6. For n = 5, 1 × 25 + 6 = 31.
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: 19, 34, 59, 94, ____
139
The nth term is 5n² + 14. For n = 5, 5 × 25 + 14 = 139.
11. 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.
12. Find the 5th term of the quadratic sequence: 4, 7, 12, 19, ____
28
The nth term is 1n² + 3. For n = 5, 1 × 25 + 3 = 28.

12 questions · Seed 104733 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Second-difference sequences

Take your time. Show your thinking.

1. Find the 5th term of the quadratic sequence: 11, 23, 43, 71, ____
2. Find the 5th term of the quadratic sequence: 6, 12, 22, 36, ____
3. Find the 5th term of the quadratic sequence: 8, 17, 32, 53, ____
4. Find the 5th term of the quadratic sequence: 10, 13, 18, 25, ____
5. Find the 5th term of the quadratic sequence: 3, 6, 11, 18, ____
6. Find the 5th term of the quadratic sequence: 17, 29, 49, 77, ____
7. Find the 5th term of the quadratic sequence: 4, 10, 20, 34, ____
8. Find the 5th term of the quadratic sequence: 7, 10, 15, 22, ____
9. Find the 5th term of the quadratic sequence: 13, 28, 53, 88, ____
10. Find the 5th term of the quadratic sequence: 19, 34, 59, 94, ____
11. Find the 5th term of the quadratic sequence: 19, 31, 51, 79, ____
12. Find the 5th term of the quadratic sequence: 4, 7, 12, 19, ____

12 questions · Seed 104733 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Second-difference sequences

Answers and reasoning. Review before teaching.

1. Find the 5th term of the quadratic sequence: 11, 23, 43, 71, ____
107
The nth term is 4n² + 7. For n = 5, 4 × 25 + 7 = 107.
2. Find the 5th term of the quadratic sequence: 6, 12, 22, 36, ____
54
The nth term is 2n² + 4. For n = 5, 2 × 25 + 4 = 54.
3. Find the 5th term of the quadratic sequence: 8, 17, 32, 53, ____
80
The nth term is 3n² + 5. For n = 5, 3 × 25 + 5 = 80.
4. Find the 5th term of the quadratic sequence: 10, 13, 18, 25, ____
34
The nth term is 1n² + 9. For n = 5, 1 × 25 + 9 = 34.
5. Find the 5th term of the quadratic sequence: 3, 6, 11, 18, ____
27
The nth term is 1n² + 2. For n = 5, 1 × 25 + 2 = 27.
6. 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.
7. 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.
8. Find the 5th term of the quadratic sequence: 7, 10, 15, 22, ____
31
The nth term is 1n² + 6. For n = 5, 1 × 25 + 6 = 31.
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: 19, 34, 59, 94, ____
139
The nth term is 5n² + 14. For n = 5, 5 × 25 + 14 = 139.
11. 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.
12. Find the 5th term of the quadratic sequence: 4, 7, 12, 19, ____
28
The nth term is 1n² + 3. For n = 5, 1 × 25 + 3 = 28.

12 questions · Seed 104733 · Age guidance, not curriculum certification