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: 12, 21, 36, 57, ____
2. Find the 5th term of the quadratic sequence: 6, 12, 22, 36, ____
3. Find the 5th term of the quadratic sequence: 16, 25, 40, 61, ____
4. Find the 5th term of the quadratic sequence: 10, 22, 42, 70, ____
5. Find the 5th term of the quadratic sequence: 12, 24, 44, 72, ____
6. Find the 5th term of the quadratic sequence: 11, 14, 19, 26, ____
7. Find the 5th term of the quadratic sequence: 10, 19, 34, 55, ____
8. Find the 5th term of the quadratic sequence: 12, 18, 28, 42, ____
9. Find the 5th term of the quadratic sequence: 13, 28, 53, 88, ____
10. Find the 5th term of the quadratic sequence: 3, 9, 19, 33, ____
11. Find the 5th term of the quadratic sequence: 12, 27, 52, 87, ____
12. Find the 5th term of the quadratic sequence: 1, 4, 9, 16, ____

12 questions · Seed 104732 · 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: 12, 21, 36, 57, ____
84
The nth term is 3n² + 9. For n = 5, 3 × 25 + 9 = 84.
2. 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.
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: 10, 22, 42, 70, ____
106
The nth term is 4n² + 6. For n = 5, 4 × 25 + 6 = 106.
5. Find the 5th term of the quadratic sequence: 12, 24, 44, 72, ____
108
The nth term is 4n² + 8. For n = 5, 4 × 25 + 8 = 108.
6. 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.
7. Find the 5th term of the quadratic sequence: 10, 19, 34, 55, ____
82
The nth term is 3n² + 7. For n = 5, 3 × 25 + 7 = 82.
8. Find the 5th term of the quadratic sequence: 12, 18, 28, 42, ____
60
The nth term is 2n² + 10. For n = 5, 2 × 25 + 10 = 60.
9. 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.
10. Find the 5th term of the quadratic sequence: 3, 9, 19, 33, ____
51
The nth term is 2n² + 1. For n = 5, 2 × 25 + 1 = 51.
11. Find the 5th term of the quadratic sequence: 12, 27, 52, 87, ____
132
The nth term is 5n² + 7. For n = 5, 5 × 25 + 7 = 132.
12. Find the 5th term of the quadratic sequence: 1, 4, 9, 16, ____
25
The nth term is 1n² + 0. For n = 5, 1 × 25 + 0 = 25.

12 questions · Seed 104732 · 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: 12, 21, 36, 57, ____
2. Find the 5th term of the quadratic sequence: 6, 12, 22, 36, ____
3. Find the 5th term of the quadratic sequence: 16, 25, 40, 61, ____
4. Find the 5th term of the quadratic sequence: 10, 22, 42, 70, ____
5. Find the 5th term of the quadratic sequence: 12, 24, 44, 72, ____
6. Find the 5th term of the quadratic sequence: 11, 14, 19, 26, ____
7. Find the 5th term of the quadratic sequence: 10, 19, 34, 55, ____
8. Find the 5th term of the quadratic sequence: 12, 18, 28, 42, ____
9. Find the 5th term of the quadratic sequence: 13, 28, 53, 88, ____
10. Find the 5th term of the quadratic sequence: 3, 9, 19, 33, ____
11. Find the 5th term of the quadratic sequence: 12, 27, 52, 87, ____
12. Find the 5th term of the quadratic sequence: 1, 4, 9, 16, ____

12 questions · Seed 104732 · 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: 12, 21, 36, 57, ____
84
The nth term is 3n² + 9. For n = 5, 3 × 25 + 9 = 84.
2. 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.
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: 10, 22, 42, 70, ____
106
The nth term is 4n² + 6. For n = 5, 4 × 25 + 6 = 106.
5. Find the 5th term of the quadratic sequence: 12, 24, 44, 72, ____
108
The nth term is 4n² + 8. For n = 5, 4 × 25 + 8 = 108.
6. 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.
7. Find the 5th term of the quadratic sequence: 10, 19, 34, 55, ____
82
The nth term is 3n² + 7. For n = 5, 3 × 25 + 7 = 82.
8. Find the 5th term of the quadratic sequence: 12, 18, 28, 42, ____
60
The nth term is 2n² + 10. For n = 5, 2 × 25 + 10 = 60.
9. 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.
10. Find the 5th term of the quadratic sequence: 3, 9, 19, 33, ____
51
The nth term is 2n² + 1. For n = 5, 2 × 25 + 1 = 51.
11. Find the 5th term of the quadratic sequence: 12, 27, 52, 87, ____
132
The nth term is 5n² + 7. For n = 5, 5 × 25 + 7 = 132.
12. Find the 5th term of the quadratic sequence: 1, 4, 9, 16, ____
25
The nth term is 1n² + 0. For n = 5, 1 × 25 + 0 = 25.

12 questions · Seed 104732 · Age guidance, not curriculum certification