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: 6, 12, 22, 36, ____
2. Find the 5th term of the quadratic sequence: 16, 31, 56, 91, ____
3. Find the 5th term of the quadratic sequence: 11, 17, 27, 41, ____
4. Find the 5th term of the quadratic sequence: 6, 15, 30, 51, ____
5. Find the 5th term of the quadratic sequence: 5, 17, 37, 65, ____
6. Find the 5th term of the quadratic sequence: 10, 19, 34, 55, ____
7. Find the 5th term of the quadratic sequence: 5, 8, 13, 20, ____
8. Find the 5th term of the quadratic sequence: 4, 16, 36, 64, ____
9. Find the 5th term of the quadratic sequence: 10, 25, 50, 85, ____
10. Find the 5th term of the quadratic sequence: 13, 22, 37, 58, ____
11. Find the 5th term of the quadratic sequence: 8, 14, 24, 38, ____
12. Find the 5th term of the quadratic sequence: 6, 18, 38, 66, ____

12 questions · Seed 104734 · 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: 16, 31, 56, 91, ____
136
The nth term is 5n² + 11. For n = 5, 5 × 25 + 11 = 136.
3. 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.
4. Find the 5th term of the quadratic sequence: 6, 15, 30, 51, ____
78
The nth term is 3n² + 3. For n = 5, 3 × 25 + 3 = 78.
5. Find the 5th term of the quadratic sequence: 5, 17, 37, 65, ____
101
The nth term is 4n² + 1. For n = 5, 4 × 25 + 1 = 101.
6. 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.
7. Find the 5th term of the quadratic sequence: 5, 8, 13, 20, ____
29
The nth term is 1n² + 4. For n = 5, 1 × 25 + 4 = 29.
8. 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.
9. Find the 5th term of the quadratic sequence: 10, 25, 50, 85, ____
130
The nth term is 5n² + 5. For n = 5, 5 × 25 + 5 = 130.
10. Find the 5th term of the quadratic sequence: 13, 22, 37, 58, ____
85
The nth term is 3n² + 10. For n = 5, 3 × 25 + 10 = 85.
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: 6, 18, 38, 66, ____
102
The nth term is 4n² + 2. For n = 5, 4 × 25 + 2 = 102.

12 questions · Seed 104734 · 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: 16, 31, 56, 91, ____
3. Find the 5th term of the quadratic sequence: 11, 17, 27, 41, ____
4. Find the 5th term of the quadratic sequence: 6, 15, 30, 51, ____
5. Find the 5th term of the quadratic sequence: 5, 17, 37, 65, ____
6. Find the 5th term of the quadratic sequence: 10, 19, 34, 55, ____
7. Find the 5th term of the quadratic sequence: 5, 8, 13, 20, ____
8. Find the 5th term of the quadratic sequence: 4, 16, 36, 64, ____
9. Find the 5th term of the quadratic sequence: 10, 25, 50, 85, ____
10. Find the 5th term of the quadratic sequence: 13, 22, 37, 58, ____
11. Find the 5th term of the quadratic sequence: 8, 14, 24, 38, ____
12. Find the 5th term of the quadratic sequence: 6, 18, 38, 66, ____

12 questions · Seed 104734 · 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: 16, 31, 56, 91, ____
136
The nth term is 5n² + 11. For n = 5, 5 × 25 + 11 = 136.
3. 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.
4. Find the 5th term of the quadratic sequence: 6, 15, 30, 51, ____
78
The nth term is 3n² + 3. For n = 5, 3 × 25 + 3 = 78.
5. Find the 5th term of the quadratic sequence: 5, 17, 37, 65, ____
101
The nth term is 4n² + 1. For n = 5, 4 × 25 + 1 = 101.
6. 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.
7. Find the 5th term of the quadratic sequence: 5, 8, 13, 20, ____
29
The nth term is 1n² + 4. For n = 5, 1 × 25 + 4 = 29.
8. 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.
9. Find the 5th term of the quadratic sequence: 10, 25, 50, 85, ____
130
The nth term is 5n² + 5. For n = 5, 5 × 25 + 5 = 130.
10. Find the 5th term of the quadratic sequence: 13, 22, 37, 58, ____
85
The nth term is 3n² + 10. For n = 5, 3 × 25 + 10 = 85.
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: 6, 18, 38, 66, ____
102
The nth term is 4n² + 2. For n = 5, 4 × 25 + 2 = 102.

12 questions · Seed 104734 · Age guidance, not curriculum certification