Sequences

Maths, Algebra. Usually met in years 7 to 11.

Continue sequences, find the nth term of a linear sequence, and spot geometric and quadratic patterns.

What you practise

Term-to-term rules
The nth term of a linear sequence
Geometric and quadratic sequences

Moves from adding the same amount each time to sequences that grow faster. Practice moves up a level when a round goes well and down when it does not.

Sample questions

Each sample comes with the method and the reason every wrong option is wrong. Real practice rounds are ten questions at your level.

Sample question, level 2 of 5

Find the nth term of the sequence 14, 20, 26, 32, ...

6n + 8
n + 8
6n
8n + 6
14n

Show the answer and method

Answer: A, 6n + 8

The method: The terms go up by 6, so it starts 6n. When n = 1, 6n = 6 but the first term is 14, so add 8: 6n + 8.

Why the other options are wrong:

B, n + 8: The number in front of n must be the difference between terms.
C, 6n: The sequence does not start at 6: the term-to-term rule gives 6n, but it needs adjusting.
D, 8n + 6: The two numbers are the wrong way round.
E, 14n: The first term was used as the number in front of n.

Sample question, level 4 of 5

What is the next term in the sequence 7, 35, 175, 875, ...?

21875
4375
880
5250
1575

Show the answer and method

Answer: B, 4375

The method: Each term is 5 times the one before. 875 × 5 = 4375.

Why the other options are wrong:

A, 21875: Multiplied by 5 twice.
C, 880: 5 was added instead of multiplying by 5.
D, 5250: Multiplied by 6 instead of 5.
E, 1575: This keeps adding the last difference, but the differences grow: the terms are multiplied by 5.

See where this fits: GCSE maths with AQA and Key Stage 3.