ReasoningAges 13-15

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 13-15

Second-difference sequences

Take your time. Show your thinking.

1. Find the 5th term of the quadratic sequence: 13, 19, 29, 43, ____
2. Find the 5th term of the quadratic sequence: 9, 18, 33, 54, ____
3. Find the 5th term of the quadratic sequence: 15, 27, 47, 75, ____
4. Find the 5th term of the quadratic sequence: 7, 16, 31, 52, ____
5. Find the 5th term of the quadratic sequence: 6, 18, 38, 66, ____
6. Find the 5th term of the quadratic sequence: 14, 29, 54, 89, ____
7. Find the 5th term of the quadratic sequence: 13, 28, 53, 88, ____
8. Find the 5th term of the quadratic sequence: 15, 24, 39, 60, ____
9. Find the 5th term of the quadratic sequence: 4, 16, 36, 64, ____
10. Find the 5th term of the quadratic sequence: 4, 13, 28, 49, ____
11. Find the 5th term of the quadratic sequence: 9, 15, 25, 39, ____
12. Find the 5th term of the quadratic sequence: 7, 13, 23, 37, ____

12 questions · Seed 53 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 13-15

Second-difference sequences

Answers and reasoning. Review before teaching.

1. Find the 5th term of the quadratic sequence: 13, 19, 29, 43, ____
61
The nth term is 2n² + 11. For n = 5, 2 × 25 + 11 = 61.
2. Find the 5th term of the quadratic sequence: 9, 18, 33, 54, ____
81
The nth term is 3n² + 6. For n = 5, 3 × 25 + 6 = 81.
3. Find the 5th term of the quadratic sequence: 15, 27, 47, 75, ____
111
The nth term is 4n² + 11. For n = 5, 4 × 25 + 11 = 111.
4. Find the 5th term of the quadratic sequence: 7, 16, 31, 52, ____
79
The nth term is 3n² + 4. For n = 5, 3 × 25 + 4 = 79.
5. 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.
6. 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.
7. Find the 5th term of the quadratic sequence: 13, 28, 53, 88, ____
133
The nth term is 5n² + 8. For n = 5, 5 × 25 + 8 = 133.
8. 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.
9. 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.
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: 9, 15, 25, 39, ____
57
The nth term is 2n² + 7. For n = 5, 2 × 25 + 7 = 57.
12. 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.

12 questions · Seed 53 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Second-difference sequences

Take your time. Show your thinking.

1. Find the 5th term of the quadratic sequence: 13, 19, 29, 43, ____
2. Find the 5th term of the quadratic sequence: 9, 18, 33, 54, ____
3. Find the 5th term of the quadratic sequence: 15, 27, 47, 75, ____
4. Find the 5th term of the quadratic sequence: 7, 16, 31, 52, ____
5. Find the 5th term of the quadratic sequence: 6, 18, 38, 66, ____
6. Find the 5th term of the quadratic sequence: 14, 29, 54, 89, ____
7. Find the 5th term of the quadratic sequence: 13, 28, 53, 88, ____
8. Find the 5th term of the quadratic sequence: 15, 24, 39, 60, ____
9. Find the 5th term of the quadratic sequence: 4, 16, 36, 64, ____
10. Find the 5th term of the quadratic sequence: 4, 13, 28, 49, ____
11. Find the 5th term of the quadratic sequence: 9, 15, 25, 39, ____
12. Find the 5th term of the quadratic sequence: 7, 13, 23, 37, ____

12 questions · Seed 53 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Second-difference sequences

Answers and reasoning. Review before teaching.

1. Find the 5th term of the quadratic sequence: 13, 19, 29, 43, ____
61
The nth term is 2n² + 11. For n = 5, 2 × 25 + 11 = 61.
2. Find the 5th term of the quadratic sequence: 9, 18, 33, 54, ____
81
The nth term is 3n² + 6. For n = 5, 3 × 25 + 6 = 81.
3. Find the 5th term of the quadratic sequence: 15, 27, 47, 75, ____
111
The nth term is 4n² + 11. For n = 5, 4 × 25 + 11 = 111.
4. Find the 5th term of the quadratic sequence: 7, 16, 31, 52, ____
79
The nth term is 3n² + 4. For n = 5, 3 × 25 + 4 = 79.
5. 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.
6. 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.
7. Find the 5th term of the quadratic sequence: 13, 28, 53, 88, ____
133
The nth term is 5n² + 8. For n = 5, 5 × 25 + 8 = 133.
8. 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.
9. 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.
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: 9, 15, 25, 39, ____
57
The nth term is 2n² + 7. For n = 5, 2 × 25 + 7 = 57.
12. 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.

12 questions · Seed 53 · Age guidance, not curriculum certification