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: 14, 17, 22, 29, ____
2. Find the 5th term of the quadratic sequence: 7, 16, 31, 52, ____
3. Find the 5th term of the quadratic sequence: 4, 13, 28, 49, ____
4. Find the 5th term of the quadratic sequence: 15, 30, 55, 90, ____
5. Find the 5th term of the quadratic sequence: 9, 21, 41, 69, ____
6. Find the 5th term of the quadratic sequence: 15, 24, 39, 60, ____
7. Find the 5th term of the quadratic sequence: 18, 30, 50, 78, ____
8. Find the 5th term of the quadratic sequence: 16, 31, 56, 91, ____
9. Find the 5th term of the quadratic sequence: 2, 8, 18, 32, ____
10. Find the 5th term of the quadratic sequence: 7, 10, 15, 22, ____
11. Find the 5th term of the quadratic sequence: 6, 12, 22, 36, ____
12. Find the 5th term of the quadratic sequence: 12, 15, 20, 27, ____

12 questions · Seed 104729 · 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: 14, 17, 22, 29, ____
38
The nth term is 1n² + 13. For n = 5, 1 × 25 + 13 = 38.
2. Find the 5th term of the quadratic sequence: 7, 16, 31, 52, ____
79
The nth term is 3n² + 4. For n = 5, 3 × 25 + 4 = 79.
3. 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.
4. 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.
5. Find the 5th term of the quadratic sequence: 9, 21, 41, 69, ____
105
The nth term is 4n² + 5. For n = 5, 4 × 25 + 5 = 105.
6. Find the 5th term of the quadratic sequence: 15, 24, 39, 60, ____
87
The nth term is 3n² + 12. For n = 5, 3 × 25 + 12 = 87.
7. Find the 5th term of the quadratic sequence: 18, 30, 50, 78, ____
114
The nth term is 4n² + 14. For n = 5, 4 × 25 + 14 = 114.
8. 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.
9. 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.
10. 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.
11. 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.
12. 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.

12 questions · Seed 104729 · 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: 14, 17, 22, 29, ____
2. Find the 5th term of the quadratic sequence: 7, 16, 31, 52, ____
3. Find the 5th term of the quadratic sequence: 4, 13, 28, 49, ____
4. Find the 5th term of the quadratic sequence: 15, 30, 55, 90, ____
5. Find the 5th term of the quadratic sequence: 9, 21, 41, 69, ____
6. Find the 5th term of the quadratic sequence: 15, 24, 39, 60, ____
7. Find the 5th term of the quadratic sequence: 18, 30, 50, 78, ____
8. Find the 5th term of the quadratic sequence: 16, 31, 56, 91, ____
9. Find the 5th term of the quadratic sequence: 2, 8, 18, 32, ____
10. Find the 5th term of the quadratic sequence: 7, 10, 15, 22, ____
11. Find the 5th term of the quadratic sequence: 6, 12, 22, 36, ____
12. Find the 5th term of the quadratic sequence: 12, 15, 20, 27, ____

12 questions · Seed 104729 · 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: 14, 17, 22, 29, ____
38
The nth term is 1n² + 13. For n = 5, 1 × 25 + 13 = 38.
2. Find the 5th term of the quadratic sequence: 7, 16, 31, 52, ____
79
The nth term is 3n² + 4. For n = 5, 3 × 25 + 4 = 79.
3. 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.
4. 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.
5. Find the 5th term of the quadratic sequence: 9, 21, 41, 69, ____
105
The nth term is 4n² + 5. For n = 5, 4 × 25 + 5 = 105.
6. Find the 5th term of the quadratic sequence: 15, 24, 39, 60, ____
87
The nth term is 3n² + 12. For n = 5, 3 × 25 + 12 = 87.
7. Find the 5th term of the quadratic sequence: 18, 30, 50, 78, ____
114
The nth term is 4n² + 14. For n = 5, 4 × 25 + 14 = 114.
8. 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.
9. 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.
10. 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.
11. 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.
12. 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.

12 questions · Seed 104729 · Age guidance, not curriculum certification