GCSE · Sequences

The nth term of a quadratic sequenceExam-style questions

Why constant SECOND differences signal an n² rule, why the n²-coefficient is HALF the second difference, and the subtract-and-conquer routine that finds the full an² + bn + c.

Start practising Read the lesson

13 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 3 Level 4 Level 5

1
The $n$ th term of a sequence is $n^2 - 3n + 5$

Work out the 6th term of the sequence.
Level 3 · 2 marksTry it
2
The $n$ th term of a sequence is $2n^2 - n$

Work out the $5$ th term of the sequence.
Level 3 · 2 marksTry it
3
Here are the first four terms of a quadratic sequence.

$5 \qquad 11 \qquad 21 \qquad 35$

Find an expression, in terms of $n$ , for the $n$ th term. (3 marks)
Level 3 · 3 marksTry it
4
Here are the first five terms of a quadratic sequence.

$3 \qquad 8 \qquad 15 \qquad 24 \qquad 35$

Find an expression, in terms of $n$ , for the $n$ th term of this sequence. (3 marks)
Level 3 · 3 marksTry it
5
Here are the first four terms of a quadratic sequence.

$4 \qquad 10 \qquad 18 \qquad 28$

Find an expression, in terms of $n$ , for the $n$ th term. [3]
Level 3 · 3 marksTry it