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: 18, 30, 50, 78, ____
2. Find the 5th term of the quadratic sequence: 16, 19, 24, 31, ____
3. Find the 5th term of the quadratic sequence: 15, 24, 39, 60, ____
4. Find the 5th term of the quadratic sequence: 14, 26, 46, 74, ____
5. Find the 5th term of the quadratic sequence: 14, 29, 54, 89, ____
6. Find the 5th term of the quadratic sequence: 4, 13, 28, 49, ____
7. Find the 5th term of the quadratic sequence: 8, 14, 24, 38, ____
8. Find the 5th term of the quadratic sequence: 4, 10, 20, 34, ____
9. Find the 5th term of the quadratic sequence: 19, 31, 51, 79, ____
10. Find the 5th term of the quadratic sequence: 7, 22, 47, 82, ____
11. Find the 5th term of the quadratic sequence: 6, 12, 22, 36, ____
12. Find the 5th term of the quadratic sequence: 13, 28, 53, 88, ____

12 questions · Seed 104735 · 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: 18, 30, 50, 78, ____
114
The nth term is 4n² + 14. For n = 5, 4 × 25 + 14 = 114.
2. Find the 5th term of the quadratic sequence: 16, 19, 24, 31, ____
40
The nth term is 1n² + 15. For n = 5, 1 × 25 + 15 = 40.
3. 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.
4. Find the 5th term of the quadratic sequence: 14, 26, 46, 74, ____
110
The nth term is 4n² + 10. For n = 5, 4 × 25 + 10 = 110.
5. 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.
6. 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.
7. Find the 5th term of the quadratic sequence: 8, 14, 24, 38, ____
56
The nth term is 2n² + 6. For n = 5, 2 × 25 + 6 = 56.
8. 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.
9. 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.
10. 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.
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: 13, 28, 53, 88, ____
133
The nth term is 5n² + 8. For n = 5, 5 × 25 + 8 = 133.

12 questions · Seed 104735 · 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: 18, 30, 50, 78, ____
2. Find the 5th term of the quadratic sequence: 16, 19, 24, 31, ____
3. Find the 5th term of the quadratic sequence: 15, 24, 39, 60, ____
4. Find the 5th term of the quadratic sequence: 14, 26, 46, 74, ____
5. Find the 5th term of the quadratic sequence: 14, 29, 54, 89, ____
6. Find the 5th term of the quadratic sequence: 4, 13, 28, 49, ____
7. Find the 5th term of the quadratic sequence: 8, 14, 24, 38, ____
8. Find the 5th term of the quadratic sequence: 4, 10, 20, 34, ____
9. Find the 5th term of the quadratic sequence: 19, 31, 51, 79, ____
10. Find the 5th term of the quadratic sequence: 7, 22, 47, 82, ____
11. Find the 5th term of the quadratic sequence: 6, 12, 22, 36, ____
12. Find the 5th term of the quadratic sequence: 13, 28, 53, 88, ____

12 questions · Seed 104735 · 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: 18, 30, 50, 78, ____
114
The nth term is 4n² + 14. For n = 5, 4 × 25 + 14 = 114.
2. Find the 5th term of the quadratic sequence: 16, 19, 24, 31, ____
40
The nth term is 1n² + 15. For n = 5, 1 × 25 + 15 = 40.
3. 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.
4. Find the 5th term of the quadratic sequence: 14, 26, 46, 74, ____
110
The nth term is 4n² + 10. For n = 5, 4 × 25 + 10 = 110.
5. 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.
6. 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.
7. Find the 5th term of the quadratic sequence: 8, 14, 24, 38, ____
56
The nth term is 2n² + 6. For n = 5, 2 × 25 + 6 = 56.
8. 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.
9. 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.
10. 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.
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: 13, 28, 53, 88, ____
133
The nth term is 5n² + 8. For n = 5, 5 × 25 + 8 = 133.

12 questions · Seed 104735 · Age guidance, not curriculum certification