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:

$4 \qquad 11 \qquad 22 \qquad 37 \qquad 56$

Find an expression, in terms of $n$ , for the $n$ th term of the sequence.
Level 5 · 4 marksTry it
2
Here are the first five terms of a quadratic sequence:

$6 \qquad 15 \qquad 28 \qquad 45 \qquad 66$

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

Is $63$ a term of this sequence? You must show your working.
Level 5 · 3 marksTry it