These exam-style quadratic sequences questions will test your knowledge on finding the 𝑛th term of quadratic sequences. You can revise how to find the 𝑛th term right here or download our FREE sequences bundle.

1. Find the 𝑛th term of the following sequence: 0, 3, 8, 15, 24, …

2. Find the 𝑛th term of the following sequence: -1, 5, 15, 29, 47, …

3. Find the 𝑛th term of the following sequence: 8, 15, 28, 47, 72, …

4. The 𝑛th term of a quadratic sequence is 5𝑛2. Justin says the 4th term will be 400. Do you agree with Justin? Explain your answer.

5. The sequence of triangular numbers starts 1, 3, 6, 10, 15, …
a. Explain why this is a quadratic sequence.
b. Find the 𝑛th term for the sequence of triangular numbers. 6. The 𝑛th term of a quadratic sequence is 𝑛2 – 4𝑛 + 3. Chris says no term of this sequence will be negative. Give an example to show that Chris is wrong.

1. Find the 𝑛th term of the following sequence: 0, 3, 8, 15, 24, …
𝑛2 – 1

2. Find the 𝑛th term of the following sequence: -1, 5, 15, 29, 47, …
2𝑛2 – 3

3. Find the 𝑛th term of the following sequence: 8, 15, 28, 47, 72, …
3𝑛2 – 2𝑛 + 7

4. The 𝑛th term of a quadratic sequence is 5𝑛2. Justin says the 4th term will be 400. Do you agree with Justin? Explain your answer.
No, if 𝑛 = 4 then 5𝑛2 = 5 × 42 which is 80 not 400.

5. The sequence of triangular numbers starts 1, 3, 6, 10, 15, …
a. Explain why this is a quadratic sequence.
The first differences are not the same (2, 3, 4, 5) but the second differences are (1, 1, 1).
b. Find the 𝑛th term for the sequence of triangular numbers.
0.5𝑛2 + 0.5𝑛

6. The 𝑛th term of a quadratic sequence is 𝑛2 – 4𝑛 + 3. Chris says no term of this sequence will be negative. Give an example to show that Chris is wrong.
When 𝑛 = 2, 𝑛2 – 4𝑛 + 3 = -1 so Chris is wrong.

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