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.

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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
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 the sequence.
Level 4 · 3 marksTry it
2
Here are the first five terms of a quadratic sequence:

$5 \qquad 11 \qquad 21 \qquad 35 \qquad 53$

Find an expression, in terms of $n$ , for the $n$ th term of the sequence.
Level 4 · 3 marksTry it
3
The $n$ th term of a sequence is $n^2 + 5$

Explain why 150 is not a term of this sequence.
Level 4 · 2 marksTry it
4
Here are the first five terms of a quadratic sequence:

$2 \qquad 5 \qquad 10 \qquad 17 \qquad 26$

Find an expression, in terms of $n$ , for the $n$ th term.
Level 4 · 3 marksTry it
5
Here are the first five terms of a quadratic sequence:

$4 \qquad 16 \qquad 36 \qquad 64 \qquad 100$

Find an expression, in terms of $n$ , for the $n$ th term.
Level 4 · 3 marksTry it