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: 17, 23, 33, 47, ____
2. Find the 5th term of the quadratic sequence: 4, 16, 36, 64, ____
3. Find the 5th term of the quadratic sequence: 5, 20, 45, 80, ____
4. Find the 5th term of the quadratic sequence: 14, 26, 46, 74, ____
5. Find the 5th term of the quadratic sequence: 11, 17, 27, 41, ____
6. Find the 5th term of the quadratic sequence: 12, 24, 44, 72, ____
7. Find the 5th term of the quadratic sequence: 18, 27, 42, 63, ____
8. Find the 5th term of the quadratic sequence: 18, 33, 58, 93, ____
9. Find the 5th term of the quadratic sequence: 16, 19, 24, 31, ____
10. Find the 5th term of the quadratic sequence: 12, 18, 28, 42, ____
11. Find the 5th term of the quadratic sequence: 8, 14, 24, 38, ____
12. Find the 5th term of the quadratic sequence: 20, 35, 60, 95, ____

12 questions · Seed 48 · 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: 17, 23, 33, 47, ____
65
The nth term is 2n² + 15. For n = 5, 2 × 25 + 15 = 65.
2. 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.
3. 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.
4. Find the 5th term of the quadratic sequence: 14, 26, 46, 74, ____
110
The nth term is 4n² + 10. For n = 5, 4 × 25 + 10 = 110.
5. Find the 5th term of the quadratic sequence: 11, 17, 27, 41, ____
59
The nth term is 2n² + 9. For n = 5, 2 × 25 + 9 = 59.
6. 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.
7. Find the 5th term of the quadratic sequence: 18, 27, 42, 63, ____
90
The nth term is 3n² + 15. For n = 5, 3 × 25 + 15 = 90.
8. 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.
9. 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.
10. 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.
11. Find the 5th term of the quadratic sequence: 8, 14, 24, 38, ____
56
The nth term is 2n² + 6. For n = 5, 2 × 25 + 6 = 56.
12. 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.

12 questions · Seed 48 · 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: 17, 23, 33, 47, ____
2. Find the 5th term of the quadratic sequence: 4, 16, 36, 64, ____
3. Find the 5th term of the quadratic sequence: 5, 20, 45, 80, ____
4. Find the 5th term of the quadratic sequence: 14, 26, 46, 74, ____
5. Find the 5th term of the quadratic sequence: 11, 17, 27, 41, ____
6. Find the 5th term of the quadratic sequence: 12, 24, 44, 72, ____
7. Find the 5th term of the quadratic sequence: 18, 27, 42, 63, ____
8. Find the 5th term of the quadratic sequence: 18, 33, 58, 93, ____
9. Find the 5th term of the quadratic sequence: 16, 19, 24, 31, ____
10. Find the 5th term of the quadratic sequence: 12, 18, 28, 42, ____
11. Find the 5th term of the quadratic sequence: 8, 14, 24, 38, ____
12. Find the 5th term of the quadratic sequence: 20, 35, 60, 95, ____

12 questions · Seed 48 · 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: 17, 23, 33, 47, ____
65
The nth term is 2n² + 15. For n = 5, 2 × 25 + 15 = 65.
2. 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.
3. 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.
4. Find the 5th term of the quadratic sequence: 14, 26, 46, 74, ____
110
The nth term is 4n² + 10. For n = 5, 4 × 25 + 10 = 110.
5. Find the 5th term of the quadratic sequence: 11, 17, 27, 41, ____
59
The nth term is 2n² + 9. For n = 5, 2 × 25 + 9 = 59.
6. 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.
7. Find the 5th term of the quadratic sequence: 18, 27, 42, 63, ____
90
The nth term is 3n² + 15. For n = 5, 3 × 25 + 15 = 90.
8. 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.
9. 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.
10. 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.
11. Find the 5th term of the quadratic sequence: 8, 14, 24, 38, ____
56
The nth term is 2n² + 6. For n = 5, 2 × 25 + 6 = 56.
12. 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.

12 questions · Seed 48 · Age guidance, not curriculum certification