## nth term of a quadratic sequence questions

… can seem extremely difficult, although in this video, I've tried to give you a fairly straightforward method to use. If you apply the same idea each time, you should be able to calculate an expression for the nth term with most of the questions in GCSE maths.

The whole idea is that you are creating an expression with the general form of “an² + bn + c.” This just means the ideal layout of the expression.

Here's the questions: QT Quadratic Sequence

Here's the answers: QT Quadratic Sequence ANSWERS

Video 1:

Here's the questions:

1. A quadratic sequence is given by Un= n^2 + 2n – 4

Write down the first six terms in the sequence. (2 marks)

2. A quadratic sequence is given by Un= n^2 + 3n

Write down the first six terms in the sequence. (2 marks)

3. The nth term of a sequence is 3n^2 + 2n – 2

Work out the 10th term of the sequence (2 marks)

4. Here are the first 6 terms of a quadratic sequence

3 6 11 18 27 38

Find an expression, in terms of n, for the nth term of this sequence. (3 marks)

5. Here are the first 5 terms of a quadratic sequence

5 9 17 29 45

Find an expression, in terms of n, for the nth term of this sequence. (3 marks)

6. Here are the first 6 terms of a quadratic sequence

2 9 22 41 66 97

Find an expression, in terms of n, for the nth term of this sequence. (3 marks)

7. Here are the first 5 terms of a quadratic sequence

18 11 -2 -21 -46 ….

Find an expression, in terms of n, for the nth term of this sequence.

(3 marks)

Calculate the 10th term in the sequence. (1 mark)

Video 2:

Here's the questions:

8. A quadratic sequence starts:

-8 2, 16 34 ….

a) Show that the nth term is 2n2+4n – 14 (3 marks)

b) Hence find the term that has the value 112. (2 marks)

9. a) Calculate the formula for the nth term of the following sequence:

-2, -1, 1, 4 …. (3 marks)

b) Calculate the 10th term in the sequence. (1 mark)

10. a) Calculate the formula for the nth term of the following sequence:

19 15 9 1 …. (3 marks)

b) Calculate the 10th term in the sequence. (1 mark)

11. The nth term of a sequence is n² + 2n + 1

Two consecutive terms in the sequence have a difference of 13.

Work out the two terms. (3 marks)

12. Here are some patterns made with square tiles.

Write an expression, in terms of n, for the number of tiles needed to make the nth pattern in this sequence. (3 marks)

Joe says that one pattern in the sequence is made from exactly 80 tiles. Is Joe correct? Give a reason for your answer. (1 mark)

## Top Tips!

- You need to show the second difference – this number is 2 x a
- The difference between the first two numbers of the sequence is 3a + b
- The first number of the sequence is a + b + c

Use all this information and you should be able to work through. Reading this text is quite difficult to understand – it's much easier when you've watched the videos!

Please note that these videos deal with quadratics – here's a link through to the post on linear sequences.

If you’d like to ask for any more detail, or you’re not sure about anything, please do ask a question in the comments section.

All best with your studies.

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