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: 13, 28, 53, 88, ____
2. Find the 5th term of the quadratic sequence: 17, 23, 33, 47, ____
3. Find the 5th term of the quadratic sequence: 12, 15, 20, 27, ____
4. Find the 5th term of the quadratic sequence: 17, 29, 49, 77, ____
5. Find the 5th term of the quadratic sequence: 18, 33, 58, 93, ____
6. Find the 5th term of the quadratic sequence: 9, 18, 33, 54, ____
7. Find the 5th term of the quadratic sequence: 15, 30, 55, 90, ____
8. Find the 5th term of the quadratic sequence: 11, 17, 27, 41, ____
9. Find the 5th term of the quadratic sequence: 6, 12, 22, 36, ____
10. Find the 5th term of the quadratic sequence: 13, 16, 21, 28, ____
11. Find the 5th term of the quadratic sequence: 5, 20, 45, 80, ____
12. Find the 5th term of the quadratic sequence: 19, 31, 51, 79, ____

12 questions · Seed 44 · 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: 13, 28, 53, 88, ____
133
The nth term is 5n² + 8. For n = 5, 5 × 25 + 8 = 133.
2. Find the 5th term of the quadratic sequence: 17, 23, 33, 47, ____
65
The nth term is 2n² + 15. For n = 5, 2 × 25 + 15 = 65.
3. 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.
4. 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.
5. Find the 5th term of the quadratic sequence: 18, 33, 58, 93, ____
138
The nth term is 5n² + 13. For n = 5, 5 × 25 + 13 = 138.
6. Find the 5th term of the quadratic sequence: 9, 18, 33, 54, ____
81
The nth term is 3n² + 6. For n = 5, 3 × 25 + 6 = 81.
7. 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.
8. Find the 5th term of the quadratic sequence: 11, 17, 27, 41, ____
59
The nth term is 2n² + 9. For n = 5, 2 × 25 + 9 = 59.
9. 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.
10. Find the 5th term of the quadratic sequence: 13, 16, 21, 28, ____
37
The nth term is 1n² + 12. For n = 5, 1 × 25 + 12 = 37.
11. Find the 5th term of the quadratic sequence: 5, 20, 45, 80, ____
125
The nth term is 5n² + 0. For n = 5, 5 × 25 + 0 = 125.
12. 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 questions · Seed 44 · 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: 13, 28, 53, 88, ____
2. Find the 5th term of the quadratic sequence: 17, 23, 33, 47, ____
3. Find the 5th term of the quadratic sequence: 12, 15, 20, 27, ____
4. Find the 5th term of the quadratic sequence: 17, 29, 49, 77, ____
5. Find the 5th term of the quadratic sequence: 18, 33, 58, 93, ____
6. Find the 5th term of the quadratic sequence: 9, 18, 33, 54, ____
7. Find the 5th term of the quadratic sequence: 15, 30, 55, 90, ____
8. Find the 5th term of the quadratic sequence: 11, 17, 27, 41, ____
9. Find the 5th term of the quadratic sequence: 6, 12, 22, 36, ____
10. Find the 5th term of the quadratic sequence: 13, 16, 21, 28, ____
11. Find the 5th term of the quadratic sequence: 5, 20, 45, 80, ____
12. Find the 5th term of the quadratic sequence: 19, 31, 51, 79, ____

12 questions · Seed 44 · 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: 13, 28, 53, 88, ____
133
The nth term is 5n² + 8. For n = 5, 5 × 25 + 8 = 133.
2. Find the 5th term of the quadratic sequence: 17, 23, 33, 47, ____
65
The nth term is 2n² + 15. For n = 5, 2 × 25 + 15 = 65.
3. 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.
4. 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.
5. Find the 5th term of the quadratic sequence: 18, 33, 58, 93, ____
138
The nth term is 5n² + 13. For n = 5, 5 × 25 + 13 = 138.
6. Find the 5th term of the quadratic sequence: 9, 18, 33, 54, ____
81
The nth term is 3n² + 6. For n = 5, 3 × 25 + 6 = 81.
7. 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.
8. Find the 5th term of the quadratic sequence: 11, 17, 27, 41, ____
59
The nth term is 2n² + 9. For n = 5, 2 × 25 + 9 = 59.
9. 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.
10. Find the 5th term of the quadratic sequence: 13, 16, 21, 28, ____
37
The nth term is 1n² + 12. For n = 5, 1 × 25 + 12 = 37.
11. Find the 5th term of the quadratic sequence: 5, 20, 45, 80, ____
125
The nth term is 5n² + 0. For n = 5, 5 × 25 + 0 = 125.
12. 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 questions · Seed 44 · Age guidance, not curriculum certification