11+ Algebra & Sequences
Early algebra and sequences reward children who can spot patterns. In the 11+ this usually means continuing a number sequence, describing its rule, or finding a missing value in a simple equation or function machine — not the formal algebra seen at GCSE.
For linear sequences (going up by the same amount each time), the difference between terms is the number in front of n. Once children see that a sequence going up in 3s always has a rule of the form '3n + something', these questions become quick and reliable marks.
What the 11+ tests in algebra & sequences
- check_circleContinuing number and shape sequences
- check_circleFinding the term-to-term rule (e.g. '+4 each time')
- check_circleFinding the nth term of a linear sequence
- check_circleSolving simple equations for a missing value
- check_circleFunction machines (input, rule, output)
- check_circleSubstituting a number into a simple expression
Worked example
A sequence starts 4, 7, 10, 13, … What is the rule for the nth term, and what is the 10th term?
- Find the common difference: each term goes up by 3, so the rule contains 3n.
- Check 3n against the first term: 3 × 1 = 3, but the term is 4, so add 1 → nth term = 3n + 1.
- For the 10th term, substitute n = 10: 3 × 10 + 1.
checkAnswer: nth term = 3n + 1; the 10th term = 31
Common mistakes to avoid
- errorWriting the nth term as just '3n' and forgetting the '+1' adjustment.
- errorConfusing the term-to-term rule ('+3') with the position-to-term rule ('3n + 1').
- errorMiscounting positions — the first term is n = 1, not n = 0.
Top tips
- lightbulbAlways find the common difference first — it is the multiplier in front of n.
- lightbulbTest your nth-term rule on the first two or three terms before trusting it.
- lightbulbFor function machines, work backwards by doing the inverse operation to find the input.
Practise algebra & sequences free
ElevenEdge gives your child adaptive algebra & sequences questions at just the right level, with a worked solution on every one. No card needed to start.
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