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: 9, 21, 41, 69, ____
2. Find the 5th term of the quadratic sequence: 19, 34, 59, 94, ____
3. Find the 5th term of the quadratic sequence: 9, 15, 25, 39, ____
4. Find the 5th term of the quadratic sequence: 15, 18, 23, 30, ____
5. Find the 5th term of the quadratic sequence: 4, 7, 12, 19, ____
6. Find the 5th term of the quadratic sequence: 5, 11, 21, 35, ____
7. Find the 5th term of the quadratic sequence: 10, 13, 18, 25, ____
8. Find the 5th term of the quadratic sequence: 4, 10, 20, 34, ____
9. Find the 5th term of the quadratic sequence: 14, 17, 22, 29, ____
10. Find the 5th term of the quadratic sequence: 18, 27, 42, 63, ____
11. Find the 5th term of the quadratic sequence: 6, 18, 38, 66, ____
12. Find the 5th term of the quadratic sequence: 15, 21, 31, 45, ____

12 questions · Seed 42 · 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: 9, 21, 41, 69, ____
105
The nth term is 4n² + 5. For n = 5, 4 × 25 + 5 = 105.
2. 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.
3. Find the 5th term of the quadratic sequence: 9, 15, 25, 39, ____
57
The nth term is 2n² + 7. For n = 5, 2 × 25 + 7 = 57.
4. Find the 5th term of the quadratic sequence: 15, 18, 23, 30, ____
39
The nth term is 1n² + 14. For n = 5, 1 × 25 + 14 = 39.
5. 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.
6. Find the 5th term of the quadratic sequence: 5, 11, 21, 35, ____
53
The nth term is 2n² + 3. For n = 5, 2 × 25 + 3 = 53.
7. 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.
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: 14, 17, 22, 29, ____
38
The nth term is 1n² + 13. For n = 5, 1 × 25 + 13 = 38.
10. Find the 5th term of the quadratic sequence: 18, 27, 42, 63, ____
90
The nth term is 3n² + 15. For n = 5, 3 × 25 + 15 = 90.
11. Find the 5th term of the quadratic sequence: 6, 18, 38, 66, ____
102
The nth term is 4n² + 2. For n = 5, 4 × 25 + 2 = 102.
12. 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 questions · Seed 42 · 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: 9, 21, 41, 69, ____
2. Find the 5th term of the quadratic sequence: 19, 34, 59, 94, ____
3. Find the 5th term of the quadratic sequence: 9, 15, 25, 39, ____
4. Find the 5th term of the quadratic sequence: 15, 18, 23, 30, ____
5. Find the 5th term of the quadratic sequence: 4, 7, 12, 19, ____
6. Find the 5th term of the quadratic sequence: 5, 11, 21, 35, ____
7. Find the 5th term of the quadratic sequence: 10, 13, 18, 25, ____
8. Find the 5th term of the quadratic sequence: 4, 10, 20, 34, ____
9. Find the 5th term of the quadratic sequence: 14, 17, 22, 29, ____
10. Find the 5th term of the quadratic sequence: 18, 27, 42, 63, ____
11. Find the 5th term of the quadratic sequence: 6, 18, 38, 66, ____
12. Find the 5th term of the quadratic sequence: 15, 21, 31, 45, ____

12 questions · Seed 42 · 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: 9, 21, 41, 69, ____
105
The nth term is 4n² + 5. For n = 5, 4 × 25 + 5 = 105.
2. 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.
3. Find the 5th term of the quadratic sequence: 9, 15, 25, 39, ____
57
The nth term is 2n² + 7. For n = 5, 2 × 25 + 7 = 57.
4. Find the 5th term of the quadratic sequence: 15, 18, 23, 30, ____
39
The nth term is 1n² + 14. For n = 5, 1 × 25 + 14 = 39.
5. 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.
6. Find the 5th term of the quadratic sequence: 5, 11, 21, 35, ____
53
The nth term is 2n² + 3. For n = 5, 2 × 25 + 3 = 53.
7. 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.
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: 14, 17, 22, 29, ____
38
The nth term is 1n² + 13. For n = 5, 1 × 25 + 13 = 38.
10. Find the 5th term of the quadratic sequence: 18, 27, 42, 63, ____
90
The nth term is 3n² + 15. For n = 5, 3 × 25 + 15 = 90.
11. Find the 5th term of the quadratic sequence: 6, 18, 38, 66, ____
102
The nth term is 4n² + 2. For n = 5, 4 × 25 + 2 = 102.
12. 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 questions · Seed 42 · Age guidance, not curriculum certification