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: 8, 23, 48, 83, ____
2. Find the 5th term of the quadratic sequence: 7, 10, 15, 22, ____
3. Find the 5th term of the quadratic sequence: 9, 24, 49, 84, ____
4. Find the 5th term of the quadratic sequence: 19, 31, 51, 79, ____
5. Find the 5th term of the quadratic sequence: 6, 9, 14, 21, ____
6. Find the 5th term of the quadratic sequence: 12, 21, 36, 57, ____
7. Find the 5th term of the quadratic sequence: 13, 28, 53, 88, ____
8. Find the 5th term of the quadratic sequence: 11, 26, 51, 86, ____
9. Find the 5th term of the quadratic sequence: 3, 6, 11, 18, ____
10. Find the 5th term of the quadratic sequence: 17, 32, 57, 92, ____
11. Find the 5th term of the quadratic sequence: 16, 19, 24, 31, ____
12. Find the 5th term of the quadratic sequence: 4, 10, 20, 34, ____

12 questions · Seed 104736 · 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: 8, 23, 48, 83, ____
128
The nth term is 5n² + 3. For n = 5, 5 × 25 + 3 = 128.
2. Find the 5th term of the quadratic sequence: 7, 10, 15, 22, ____
31
The nth term is 1n² + 6. For n = 5, 1 × 25 + 6 = 31.
3. Find the 5th term of the quadratic sequence: 9, 24, 49, 84, ____
129
The nth term is 5n² + 4. For n = 5, 5 × 25 + 4 = 129.
4. 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.
5. 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.
6. 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.
7. 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.
8. Find the 5th term of the quadratic sequence: 11, 26, 51, 86, ____
131
The nth term is 5n² + 6. For n = 5, 5 × 25 + 6 = 131.
9. Find the 5th term of the quadratic sequence: 3, 6, 11, 18, ____
27
The nth term is 1n² + 2. For n = 5, 1 × 25 + 2 = 27.
10. Find the 5th term of the quadratic sequence: 17, 32, 57, 92, ____
137
The nth term is 5n² + 12. For n = 5, 5 × 25 + 12 = 137.
11. Find the 5th term of the quadratic sequence: 16, 19, 24, 31, ____
40
The nth term is 1n² + 15. For n = 5, 1 × 25 + 15 = 40.
12. 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.

12 questions · Seed 104736 · 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: 8, 23, 48, 83, ____
2. Find the 5th term of the quadratic sequence: 7, 10, 15, 22, ____
3. Find the 5th term of the quadratic sequence: 9, 24, 49, 84, ____
4. Find the 5th term of the quadratic sequence: 19, 31, 51, 79, ____
5. Find the 5th term of the quadratic sequence: 6, 9, 14, 21, ____
6. Find the 5th term of the quadratic sequence: 12, 21, 36, 57, ____
7. Find the 5th term of the quadratic sequence: 13, 28, 53, 88, ____
8. Find the 5th term of the quadratic sequence: 11, 26, 51, 86, ____
9. Find the 5th term of the quadratic sequence: 3, 6, 11, 18, ____
10. Find the 5th term of the quadratic sequence: 17, 32, 57, 92, ____
11. Find the 5th term of the quadratic sequence: 16, 19, 24, 31, ____
12. Find the 5th term of the quadratic sequence: 4, 10, 20, 34, ____

12 questions · Seed 104736 · 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: 8, 23, 48, 83, ____
128
The nth term is 5n² + 3. For n = 5, 5 × 25 + 3 = 128.
2. Find the 5th term of the quadratic sequence: 7, 10, 15, 22, ____
31
The nth term is 1n² + 6. For n = 5, 1 × 25 + 6 = 31.
3. Find the 5th term of the quadratic sequence: 9, 24, 49, 84, ____
129
The nth term is 5n² + 4. For n = 5, 5 × 25 + 4 = 129.
4. 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.
5. 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.
6. 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.
7. 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.
8. Find the 5th term of the quadratic sequence: 11, 26, 51, 86, ____
131
The nth term is 5n² + 6. For n = 5, 5 × 25 + 6 = 131.
9. Find the 5th term of the quadratic sequence: 3, 6, 11, 18, ____
27
The nth term is 1n² + 2. For n = 5, 1 × 25 + 2 = 27.
10. Find the 5th term of the quadratic sequence: 17, 32, 57, 92, ____
137
The nth term is 5n² + 12. For n = 5, 5 × 25 + 12 = 137.
11. Find the 5th term of the quadratic sequence: 16, 19, 24, 31, ____
40
The nth term is 1n² + 15. For n = 5, 1 × 25 + 15 = 40.
12. 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.

12 questions · Seed 104736 · Age guidance, not curriculum certification