GCSE · Sequences

The nth term of a linear sequenceExam-style questions

Why a constant difference makes a sequence "dn + something", how the zeroth term pins down the constant, and how the nth term answers "is 122 in this sequence?" with an equation instead of a hunch.

Start practising Read the lesson

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

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

1
Here are the first four terms of an arithmetic sequence:

$5 \qquad 8 \qquad 11 \qquad 14$

(a) Find an expression, in terms of $n$ , for the $n$ th term.

(b) Work out the $20$ th term.
Level 2 · 3 marksTry it
2
Find the $n$ th term of the sequence $\quad 4, \; 7, \; 10, \; 13, \; \ldots$
Level 2 · 2 marksTry it
3
The $n$ th term of a sequence is $3n + 2$

(a) Is $89$ a term of this sequence? You must show how you decide. (2 marks)

(b) Write down the first three terms of the sequence with $n$ th term $n^2 - 1$ (1 mark)
Level 2 · 3 marksTry it
4
Here are the first five terms of an arithmetic sequence.

$7 \qquad 11 \qquad 15 \qquad 19 \qquad 23$
(a) Find an expression, in terms of $n$ , for the $n$ th term of this sequence. (2 marks)
(b) Explain why $200$ is not a term of this sequence. (1 mark)
Level 2 · 3 marksTry it