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.

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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
The first four terms of an arithmetic sequence are:

$3 \qquad 8 \qquad 13 \qquad 18$

Explain why 122 is not a term of this sequence.
Level 4 · 3 marksTry it
2
Here are the first three patterns in a sequence made from sticks.Diagram NOT accurately drawn

Pattern 1 uses 4 sticks, Pattern 2 uses 7 sticks and Pattern 3 uses 10 sticks.

(a) Work out how many sticks are needed for Pattern 10.

(b) Explain why there is no pattern in this sequence that uses exactly 57 sticks.
Level 4 · 4 marksTry it
3
The $n$ th term of a sequence is $6n - 4$

Is $200$ a term of this sequence? You must show your working.
Level 4 · 3 marksTry it
4
The $n$ th term of a sequence is $7n + 3$

Find the first term of the sequence that is greater than $100$ .
Level 4 · 3 marksTry it