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: 20, 35, 60, 95, ____
2. Find the 5th term of the quadratic sequence: 6, 21, 46, 81, ____
3. Find the 5th term of the quadratic sequence: 6, 9, 14, 21, ____
4. Find the 5th term of the quadratic sequence: 12, 27, 52, 87, ____
5. Find the 5th term of the quadratic sequence: 11, 23, 43, 71, ____
6. Find the 5th term of the quadratic sequence: 13, 28, 53, 88, ____
7. Find the 5th term of the quadratic sequence: 4, 13, 28, 49, ____
8. Find the 5th term of the quadratic sequence: 12, 24, 44, 72, ____
9. Find the 5th term of the quadratic sequence: 12, 21, 36, 57, ____
10. Find the 5th term of the quadratic sequence: 13, 25, 45, 73, ____
11. Find the 5th term of the quadratic sequence: 5, 14, 29, 50, ____
12. Find the 5th term of the quadratic sequence: 9, 21, 41, 69, ____

12 questions · Seed 52 · 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: 20, 35, 60, 95, ____
140
The nth term is 5n² + 15. For n = 5, 5 × 25 + 15 = 140.
2. 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.
3. 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.
4. 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.
5. Find the 5th term of the quadratic sequence: 11, 23, 43, 71, ____
107
The nth term is 4n² + 7. For n = 5, 4 × 25 + 7 = 107.
6. 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.
7. Find the 5th term of the quadratic sequence: 4, 13, 28, 49, ____
76
The nth term is 3n² + 1. For n = 5, 3 × 25 + 1 = 76.
8. 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.
9. 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.
10. Find the 5th term of the quadratic sequence: 13, 25, 45, 73, ____
109
The nth term is 4n² + 9. For n = 5, 4 × 25 + 9 = 109.
11. 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.
12. 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 questions · Seed 52 · 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: 20, 35, 60, 95, ____
2. Find the 5th term of the quadratic sequence: 6, 21, 46, 81, ____
3. Find the 5th term of the quadratic sequence: 6, 9, 14, 21, ____
4. Find the 5th term of the quadratic sequence: 12, 27, 52, 87, ____
5. Find the 5th term of the quadratic sequence: 11, 23, 43, 71, ____
6. Find the 5th term of the quadratic sequence: 13, 28, 53, 88, ____
7. Find the 5th term of the quadratic sequence: 4, 13, 28, 49, ____
8. Find the 5th term of the quadratic sequence: 12, 24, 44, 72, ____
9. Find the 5th term of the quadratic sequence: 12, 21, 36, 57, ____
10. Find the 5th term of the quadratic sequence: 13, 25, 45, 73, ____
11. Find the 5th term of the quadratic sequence: 5, 14, 29, 50, ____
12. Find the 5th term of the quadratic sequence: 9, 21, 41, 69, ____

12 questions · Seed 52 · 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: 20, 35, 60, 95, ____
140
The nth term is 5n² + 15. For n = 5, 5 × 25 + 15 = 140.
2. 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.
3. 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.
4. 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.
5. Find the 5th term of the quadratic sequence: 11, 23, 43, 71, ____
107
The nth term is 4n² + 7. For n = 5, 4 × 25 + 7 = 107.
6. 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.
7. Find the 5th term of the quadratic sequence: 4, 13, 28, 49, ____
76
The nth term is 3n² + 1. For n = 5, 3 × 25 + 1 = 76.
8. 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.
9. 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.
10. Find the 5th term of the quadratic sequence: 13, 25, 45, 73, ____
109
The nth term is 4n² + 9. For n = 5, 4 × 25 + 9 = 109.
11. 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.
12. 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 questions · Seed 52 · Age guidance, not curriculum certification