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.

New variation Try interactive challenge Browse templates

Age band:Ages 13-15 Ages 16-18

Choose “Save as PDF” to keep a copy. Use your browser’s paper setting for A4 or Letter.

Worksheet StudioPractice pack · Ages 16-18

Second-difference sequences

Take your time. Show your thinking.

1. Find the 5th term of the quadratic sequence: 6, 12, 22, 36, ____
2. Find the 5th term of the quadratic sequence: 12, 18, 28, 42, ____
3. Find the 5th term of the quadratic sequence: 10, 16, 26, 40, ____
4. Find the 5th term of the quadratic sequence: 11, 14, 19, 26, ____
5. Find the 5th term of the quadratic sequence: 20, 35, 60, 95, ____
6. Find the 5th term of the quadratic sequence: 14, 23, 38, 59, ____
7. Find the 5th term of the quadratic sequence: 7, 19, 39, 67, ____
8. Find the 5th term of the quadratic sequence: 4, 10, 20, 34, ____
9. Find the 5th term of the quadratic sequence: 15, 30, 55, 90, ____
10. Find the 5th term of the quadratic sequence: 1, 4, 9, 16, ____
11. Find the 5th term of the quadratic sequence: 9, 21, 41, 69, ____
12. Find the 5th term of the quadratic sequence: 12, 24, 44, 72, ____

12 questions · Seed 50 · 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: 6, 12, 22, 36, ____
54
The nth term is 2n² + 4. For n = 5, 2 × 25 + 4 = 54.
2. 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.
3. Find the 5th term of the quadratic sequence: 10, 16, 26, 40, ____
58
The nth term is 2n² + 8. For n = 5, 2 × 25 + 8 = 58.
4. 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.
5. Find the 5th term of the quadratic sequence: 20, 35, 60, 95, ____
140
The nth term is 5n² + 15. For n = 5, 5 × 25 + 15 = 140.
6. Find the 5th term of the quadratic sequence: 14, 23, 38, 59, ____
86
The nth term is 3n² + 11. For n = 5, 3 × 25 + 11 = 86.
7. 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.
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: 15, 30, 55, 90, ____
135
The nth term is 5n² + 10. For n = 5, 5 × 25 + 10 = 135.
10. 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.
11. 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.
12. 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.

12 questions · Seed 50 · 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: 6, 12, 22, 36, ____
2. Find the 5th term of the quadratic sequence: 12, 18, 28, 42, ____
3. Find the 5th term of the quadratic sequence: 10, 16, 26, 40, ____
4. Find the 5th term of the quadratic sequence: 11, 14, 19, 26, ____
5. Find the 5th term of the quadratic sequence: 20, 35, 60, 95, ____
6. Find the 5th term of the quadratic sequence: 14, 23, 38, 59, ____
7. Find the 5th term of the quadratic sequence: 7, 19, 39, 67, ____
8. Find the 5th term of the quadratic sequence: 4, 10, 20, 34, ____
9. Find the 5th term of the quadratic sequence: 15, 30, 55, 90, ____
10. Find the 5th term of the quadratic sequence: 1, 4, 9, 16, ____
11. Find the 5th term of the quadratic sequence: 9, 21, 41, 69, ____
12. Find the 5th term of the quadratic sequence: 12, 24, 44, 72, ____

12 questions · Seed 50 · 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: 6, 12, 22, 36, ____
54
The nth term is 2n² + 4. For n = 5, 2 × 25 + 4 = 54.
2. 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.
3. Find the 5th term of the quadratic sequence: 10, 16, 26, 40, ____
58
The nth term is 2n² + 8. For n = 5, 2 × 25 + 8 = 58.
4. 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.
5. Find the 5th term of the quadratic sequence: 20, 35, 60, 95, ____
140
The nth term is 5n² + 15. For n = 5, 5 × 25 + 15 = 140.
6. Find the 5th term of the quadratic sequence: 14, 23, 38, 59, ____
86
The nth term is 3n² + 11. For n = 5, 3 × 25 + 11 = 86.
7. 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.
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: 15, 30, 55, 90, ____
135
The nth term is 5n² + 10. For n = 5, 5 × 25 + 10 = 135.
10. 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.
11. 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.
12. 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.

12 questions · Seed 50 · Age guidance, not curriculum certification