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: 17, 29, 49, 77, ____
2. Find the 5th term of the quadratic sequence: 10, 13, 18, 25, ____
3. Find the 5th term of the quadratic sequence: 16, 25, 40, 61, ____
4. Find the 5th term of the quadratic sequence: 13, 19, 29, 43, ____
5. Find the 5th term of the quadratic sequence: 11, 14, 19, 26, ____
6. Find the 5th term of the quadratic sequence: 13, 25, 45, 73, ____
7. Find the 5th term of the quadratic sequence: 14, 20, 30, 44, ____
8. Find the 5th term of the quadratic sequence: 6, 9, 14, 21, ____
9. Find the 5th term of the quadratic sequence: 6, 21, 46, 81, ____
10. Find the 5th term of the quadratic sequence: 10, 25, 50, 85, ____
11. Find the 5th term of the quadratic sequence: 15, 21, 31, 45, ____
12. Find the 5th term of the quadratic sequence: 4, 7, 12, 19, ____

12 questions · Seed 43 · 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: 17, 29, 49, 77, ____
113
The nth term is 4n² + 13. For n = 5, 4 × 25 + 13 = 113.
2. 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.
3. 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.
4. 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.
5. 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.
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: 14, 20, 30, 44, ____
62
The nth term is 2n² + 12. For n = 5, 2 × 25 + 12 = 62.
8. Find the 5th term of the quadratic sequence: 6, 9, 14, 21, ____
30
The nth term is 1n² + 5. For n = 5, 1 × 25 + 5 = 30.
9. Find the 5th term of the quadratic sequence: 6, 21, 46, 81, ____
126
The nth term is 5n² + 1. For n = 5, 5 × 25 + 1 = 126.
10. Find the 5th term of the quadratic sequence: 10, 25, 50, 85, ____
130
The nth term is 5n² + 5. For n = 5, 5 × 25 + 5 = 130.
11. Find the 5th term of the quadratic sequence: 15, 21, 31, 45, ____
63
The nth term is 2n² + 13. For n = 5, 2 × 25 + 13 = 63.
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 43 · 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: 17, 29, 49, 77, ____
2. Find the 5th term of the quadratic sequence: 10, 13, 18, 25, ____
3. Find the 5th term of the quadratic sequence: 16, 25, 40, 61, ____
4. Find the 5th term of the quadratic sequence: 13, 19, 29, 43, ____
5. Find the 5th term of the quadratic sequence: 11, 14, 19, 26, ____
6. Find the 5th term of the quadratic sequence: 13, 25, 45, 73, ____
7. Find the 5th term of the quadratic sequence: 14, 20, 30, 44, ____
8. Find the 5th term of the quadratic sequence: 6, 9, 14, 21, ____
9. Find the 5th term of the quadratic sequence: 6, 21, 46, 81, ____
10. Find the 5th term of the quadratic sequence: 10, 25, 50, 85, ____
11. Find the 5th term of the quadratic sequence: 15, 21, 31, 45, ____
12. Find the 5th term of the quadratic sequence: 4, 7, 12, 19, ____

12 questions · Seed 43 · 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: 17, 29, 49, 77, ____
113
The nth term is 4n² + 13. For n = 5, 4 × 25 + 13 = 113.
2. 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.
3. 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.
4. 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.
5. 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.
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: 14, 20, 30, 44, ____
62
The nth term is 2n² + 12. For n = 5, 2 × 25 + 12 = 62.
8. Find the 5th term of the quadratic sequence: 6, 9, 14, 21, ____
30
The nth term is 1n² + 5. For n = 5, 1 × 25 + 5 = 30.
9. Find the 5th term of the quadratic sequence: 6, 21, 46, 81, ____
126
The nth term is 5n² + 1. For n = 5, 5 × 25 + 1 = 126.
10. Find the 5th term of the quadratic sequence: 10, 25, 50, 85, ____
130
The nth term is 5n² + 5. For n = 5, 5 × 25 + 5 = 130.
11. Find the 5th term of the quadratic sequence: 15, 21, 31, 45, ____
63
The nth term is 2n² + 13. For n = 5, 2 × 25 + 13 = 63.
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 43 · Age guidance, not curriculum certification