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: 5, 14, 29, 50, ____
2. Find the 5th term of the quadratic sequence: 10, 16, 26, 40, ____
3. Find the 5th term of the quadratic sequence: 3, 12, 27, 48, ____
4. Find the 5th term of the quadratic sequence: 5, 20, 45, 80, ____
5. Find the 5th term of the quadratic sequence: 17, 23, 33, 47, ____
6. Find the 5th term of the quadratic sequence: 2, 8, 18, 32, ____
7. Find the 5th term of the quadratic sequence: 18, 33, 58, 93, ____
8. Find the 5th term of the quadratic sequence: 7, 19, 39, 67, ____
9. Find the 5th term of the quadratic sequence: 19, 34, 59, 94, ____
10. Find the 5th term of the quadratic sequence: 4, 13, 28, 49, ____
11. Find the 5th term of the quadratic sequence: 10, 19, 34, 55, ____
12. Find the 5th term of the quadratic sequence: 14, 23, 38, 59, ____

12 questions · Seed 104730 · 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: 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: 10, 16, 26, 40, ____
58
The nth term is 2n² + 8. For n = 5, 2 × 25 + 8 = 58.
3. Find the 5th term of the quadratic sequence: 3, 12, 27, 48, ____
75
The nth term is 3n² + 0. For n = 5, 3 × 25 + 0 = 75.
4. 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.
5. 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.
6. Find the 5th term of the quadratic sequence: 2, 8, 18, 32, ____
50
The nth term is 2n² + 0. For n = 5, 2 × 25 + 0 = 50.
7. 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.
8. 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.
9. 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.
10. 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.
11. Find the 5th term of the quadratic sequence: 10, 19, 34, 55, ____
82
The nth term is 3n² + 7. For n = 5, 3 × 25 + 7 = 82.
12. 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.

12 questions · Seed 104730 · 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: 5, 14, 29, 50, ____
2. Find the 5th term of the quadratic sequence: 10, 16, 26, 40, ____
3. Find the 5th term of the quadratic sequence: 3, 12, 27, 48, ____
4. Find the 5th term of the quadratic sequence: 5, 20, 45, 80, ____
5. Find the 5th term of the quadratic sequence: 17, 23, 33, 47, ____
6. Find the 5th term of the quadratic sequence: 2, 8, 18, 32, ____
7. Find the 5th term of the quadratic sequence: 18, 33, 58, 93, ____
8. Find the 5th term of the quadratic sequence: 7, 19, 39, 67, ____
9. Find the 5th term of the quadratic sequence: 19, 34, 59, 94, ____
10. Find the 5th term of the quadratic sequence: 4, 13, 28, 49, ____
11. Find the 5th term of the quadratic sequence: 10, 19, 34, 55, ____
12. Find the 5th term of the quadratic sequence: 14, 23, 38, 59, ____

12 questions · Seed 104730 · 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: 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: 10, 16, 26, 40, ____
58
The nth term is 2n² + 8. For n = 5, 2 × 25 + 8 = 58.
3. Find the 5th term of the quadratic sequence: 3, 12, 27, 48, ____
75
The nth term is 3n² + 0. For n = 5, 3 × 25 + 0 = 75.
4. 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.
5. 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.
6. Find the 5th term of the quadratic sequence: 2, 8, 18, 32, ____
50
The nth term is 2n² + 0. For n = 5, 2 × 25 + 0 = 50.
7. 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.
8. 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.
9. 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.
10. 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.
11. Find the 5th term of the quadratic sequence: 10, 19, 34, 55, ____
82
The nth term is 3n² + 7. For n = 5, 3 × 25 + 7 = 82.
12. 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.

12 questions · Seed 104730 · Age guidance, not curriculum certification