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: 2, 8, 18, 32, ____
2. Find the 5th term of the quadratic sequence: 12, 24, 44, 72, ____
3. Find the 5th term of the quadratic sequence: 10, 25, 50, 85, ____
4. Find the 5th term of the quadratic sequence: 6, 21, 46, 81, ____
5. Find the 5th term of the quadratic sequence: 7, 19, 39, 67, ____
6. Find the 5th term of the quadratic sequence: 15, 30, 55, 90, ____
7. Find the 5th term of the quadratic sequence: 15, 21, 31, 45, ____
8. Find the 5th term of the quadratic sequence: 14, 29, 54, 89, ____
9. Find the 5th term of the quadratic sequence: 9, 15, 25, 39, ____
10. Find the 5th term of the quadratic sequence: 10, 16, 26, 40, ____
11. Find the 5th term of the quadratic sequence: 8, 11, 16, 23, ____
12. Find the 5th term of the quadratic sequence: 16, 31, 56, 91, ____

12 questions · Seed 46 · 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: 2, 8, 18, 32, ____
50
The nth term is 2n² + 0. For n = 5, 2 × 25 + 0 = 50.
2. 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.
3. 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.
4. 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.
5. 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.
6. 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.
7. Find the 5th term of the quadratic sequence: 15, 21, 31, 45, ____
63
The nth term is 2n² + 13. For n = 5, 2 × 25 + 13 = 63.
8. Find the 5th term of the quadratic sequence: 14, 29, 54, 89, ____
134
The nth term is 5n² + 9. For n = 5, 5 × 25 + 9 = 134.
9. Find the 5th term of the quadratic sequence: 9, 15, 25, 39, ____
57
The nth term is 2n² + 7. For n = 5, 2 × 25 + 7 = 57.
10. 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.
11. Find the 5th term of the quadratic sequence: 8, 11, 16, 23, ____
32
The nth term is 1n² + 7. For n = 5, 1 × 25 + 7 = 32.
12. 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.

12 questions · Seed 46 · 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: 2, 8, 18, 32, ____
2. Find the 5th term of the quadratic sequence: 12, 24, 44, 72, ____
3. Find the 5th term of the quadratic sequence: 10, 25, 50, 85, ____
4. Find the 5th term of the quadratic sequence: 6, 21, 46, 81, ____
5. Find the 5th term of the quadratic sequence: 7, 19, 39, 67, ____
6. Find the 5th term of the quadratic sequence: 15, 30, 55, 90, ____
7. Find the 5th term of the quadratic sequence: 15, 21, 31, 45, ____
8. Find the 5th term of the quadratic sequence: 14, 29, 54, 89, ____
9. Find the 5th term of the quadratic sequence: 9, 15, 25, 39, ____
10. Find the 5th term of the quadratic sequence: 10, 16, 26, 40, ____
11. Find the 5th term of the quadratic sequence: 8, 11, 16, 23, ____
12. Find the 5th term of the quadratic sequence: 16, 31, 56, 91, ____

12 questions · Seed 46 · 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: 2, 8, 18, 32, ____
50
The nth term is 2n² + 0. For n = 5, 2 × 25 + 0 = 50.
2. 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.
3. 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.
4. 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.
5. 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.
6. 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.
7. Find the 5th term of the quadratic sequence: 15, 21, 31, 45, ____
63
The nth term is 2n² + 13. For n = 5, 2 × 25 + 13 = 63.
8. Find the 5th term of the quadratic sequence: 14, 29, 54, 89, ____
134
The nth term is 5n² + 9. For n = 5, 5 × 25 + 9 = 134.
9. Find the 5th term of the quadratic sequence: 9, 15, 25, 39, ____
57
The nth term is 2n² + 7. For n = 5, 2 × 25 + 7 = 57.
10. 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.
11. Find the 5th term of the quadratic sequence: 8, 11, 16, 23, ____
32
The nth term is 1n² + 7. For n = 5, 1 × 25 + 7 = 32.
12. 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.

12 questions · Seed 46 · Age guidance, not curriculum certification