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: 5, 14, 29, 50, ____
2. Find the 5th term of the quadratic sequence: 7, 19, 39, 67, ____
3. Find the 5th term of the quadratic sequence: 10, 25, 50, 85, ____
4. Find the 5th term of the quadratic sequence: 15, 30, 55, 90, ____
5. Find the 5th term of the quadratic sequence: 4, 16, 36, 64, ____
6. Find the 5th term of the quadratic sequence: 18, 33, 58, 93, ____
7. Find the 5th term of the quadratic sequence: 19, 34, 59, 94, ____
8. Find the 5th term of the quadratic sequence: 6, 21, 46, 81, ____
9. Find the 5th term of the quadratic sequence: 5, 20, 45, 80, ____
10. Find the 5th term of the quadratic sequence: 15, 24, 39, 60, ____
11. Find the 5th term of the quadratic sequence: 12, 15, 20, 27, ____
12. Find the 5th term of the quadratic sequence: 8, 11, 16, 23, ____

12 questions · Seed 45 · 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: 5, 14, 29, 50, ____
77
The nth term is 3n² + 2. For n = 5, 3 × 25 + 2 = 77.
2. Find the 5th term of the quadratic sequence: 7, 19, 39, 67, ____
103
The nth term is 4n² + 3. For n = 5, 4 × 25 + 3 = 103.
3. 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.
4. 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.
5. Find the 5th term of the quadratic sequence: 4, 16, 36, 64, ____
100
The nth term is 4n² + 0. For n = 5, 4 × 25 + 0 = 100.
6. 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.
7. 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.
8. 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.
9. 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.
10. 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.
11. 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.
12. Find the 5th term of the quadratic sequence: 8, 11, 16, 23, ____
32
The nth term is 1n² + 7. For n = 5, 1 × 25 + 7 = 32.

12 questions · Seed 45 · 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: 5, 14, 29, 50, ____
2. Find the 5th term of the quadratic sequence: 7, 19, 39, 67, ____
3. Find the 5th term of the quadratic sequence: 10, 25, 50, 85, ____
4. Find the 5th term of the quadratic sequence: 15, 30, 55, 90, ____
5. Find the 5th term of the quadratic sequence: 4, 16, 36, 64, ____
6. Find the 5th term of the quadratic sequence: 18, 33, 58, 93, ____
7. Find the 5th term of the quadratic sequence: 19, 34, 59, 94, ____
8. Find the 5th term of the quadratic sequence: 6, 21, 46, 81, ____
9. Find the 5th term of the quadratic sequence: 5, 20, 45, 80, ____
10. Find the 5th term of the quadratic sequence: 15, 24, 39, 60, ____
11. Find the 5th term of the quadratic sequence: 12, 15, 20, 27, ____
12. Find the 5th term of the quadratic sequence: 8, 11, 16, 23, ____

12 questions · Seed 45 · 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: 5, 14, 29, 50, ____
77
The nth term is 3n² + 2. For n = 5, 3 × 25 + 2 = 77.
2. Find the 5th term of the quadratic sequence: 7, 19, 39, 67, ____
103
The nth term is 4n² + 3. For n = 5, 4 × 25 + 3 = 103.
3. 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.
4. 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.
5. Find the 5th term of the quadratic sequence: 4, 16, 36, 64, ____
100
The nth term is 4n² + 0. For n = 5, 4 × 25 + 0 = 100.
6. 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.
7. 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.
8. 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.
9. 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.
10. 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.
11. 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.
12. Find the 5th term of the quadratic sequence: 8, 11, 16, 23, ____
32
The nth term is 1n² + 7. For n = 5, 1 × 25 + 7 = 32.

12 questions · Seed 45 · Age guidance, not curriculum certification