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, 17, 37, 65, ____
2. Find the 5th term of the quadratic sequence: 11, 14, 19, 26, ____
3. Find the 5th term of the quadratic sequence: 15, 24, 39, 60, ____
4. Find the 5th term of the quadratic sequence: 13, 25, 45, 73, ____
5. Find the 5th term of the quadratic sequence: 7, 13, 23, 37, ____
6. Find the 5th term of the quadratic sequence: 3, 12, 27, 48, ____
7. Find the 5th term of the quadratic sequence: 12, 15, 20, 27, ____
8. Find the 5th term of the quadratic sequence: 12, 24, 44, 72, ____
9. Find the 5th term of the quadratic sequence: 5, 14, 29, 50, ____
10. Find the 5th term of the quadratic sequence: 9, 24, 49, 84, ____
11. Find the 5th term of the quadratic sequence: 16, 31, 56, 91, ____
12. Find the 5th term of the quadratic sequence: 14, 23, 38, 59, ____

12 questions · Seed 104731 · 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, 17, 37, 65, ____
101
The nth term is 4n² + 1. For n = 5, 4 × 25 + 1 = 101.
2. Find the 5th term of the quadratic sequence: 11, 14, 19, 26, ____
35
The nth term is 1n² + 10. For n = 5, 1 × 25 + 10 = 35.
3. Find the 5th term of the quadratic sequence: 15, 24, 39, 60, ____
87
The nth term is 3n² + 12. For n = 5, 3 × 25 + 12 = 87.
4. 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.
5. Find the 5th term of the quadratic sequence: 7, 13, 23, 37, ____
55
The nth term is 2n² + 5. For n = 5, 2 × 25 + 5 = 55.
6. 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.
7. Find the 5th term of the quadratic sequence: 12, 15, 20, 27, ____
36
The nth term is 1n² + 11. For n = 5, 1 × 25 + 11 = 36.
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: 5, 14, 29, 50, ____
77
The nth term is 3n² + 2. For n = 5, 3 × 25 + 2 = 77.
10. Find the 5th term of the quadratic sequence: 9, 24, 49, 84, ____
129
The nth term is 5n² + 4. For n = 5, 5 × 25 + 4 = 129.
11. 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. 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 104731 · 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, 17, 37, 65, ____
2. Find the 5th term of the quadratic sequence: 11, 14, 19, 26, ____
3. Find the 5th term of the quadratic sequence: 15, 24, 39, 60, ____
4. Find the 5th term of the quadratic sequence: 13, 25, 45, 73, ____
5. Find the 5th term of the quadratic sequence: 7, 13, 23, 37, ____
6. Find the 5th term of the quadratic sequence: 3, 12, 27, 48, ____
7. Find the 5th term of the quadratic sequence: 12, 15, 20, 27, ____
8. Find the 5th term of the quadratic sequence: 12, 24, 44, 72, ____
9. Find the 5th term of the quadratic sequence: 5, 14, 29, 50, ____
10. Find the 5th term of the quadratic sequence: 9, 24, 49, 84, ____
11. Find the 5th term of the quadratic sequence: 16, 31, 56, 91, ____
12. Find the 5th term of the quadratic sequence: 14, 23, 38, 59, ____

12 questions · Seed 104731 · 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, 17, 37, 65, ____
101
The nth term is 4n² + 1. For n = 5, 4 × 25 + 1 = 101.
2. Find the 5th term of the quadratic sequence: 11, 14, 19, 26, ____
35
The nth term is 1n² + 10. For n = 5, 1 × 25 + 10 = 35.
3. Find the 5th term of the quadratic sequence: 15, 24, 39, 60, ____
87
The nth term is 3n² + 12. For n = 5, 3 × 25 + 12 = 87.
4. 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.
5. Find the 5th term of the quadratic sequence: 7, 13, 23, 37, ____
55
The nth term is 2n² + 5. For n = 5, 2 × 25 + 5 = 55.
6. 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.
7. Find the 5th term of the quadratic sequence: 12, 15, 20, 27, ____
36
The nth term is 1n² + 11. For n = 5, 1 × 25 + 11 = 36.
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: 5, 14, 29, 50, ____
77
The nth term is 3n² + 2. For n = 5, 3 × 25 + 2 = 77.
10. Find the 5th term of the quadratic sequence: 9, 24, 49, 84, ____
129
The nth term is 5n² + 4. For n = 5, 5 × 25 + 4 = 129.
11. 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. 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 104731 · Age guidance, not curriculum certification