Patterns and Sequences

2, 6, ?, 54, 162 — check whether you add or multiply from one term to the next. 6 ÷ 2 = 3 and 162 ÷ 54 = 3, so every term is ×3. The missing term is just 6 × 3.

Geometric (multiply-by-constant) sequences appear in the very easy band of Selective MR. They’re quick marks for students who check ratios rather than differences, and a trap for those who assume every pattern is arithmetic (adding).

The examiner checks whether students recognise a ×3 geometric pattern rather than an arithmetic one (+4 between 2 and 6 is a red herring), and simply multiply the previous term by 3.

A number sequence with one term replaced by a symbol. The pattern is geometric (multiply by a constant). Students find the missing term.

Repeating and growing patterns on Selective MR often ask for the 30th or 100th item — never count one-by-one when you can find which block it lands in.

Bead- and object-pattern questions appear regularly in the easy band of Selective MR — students who spot how group sizes grow save time and avoid miscounts.

The examiner checks whether you can partition the pattern into labelled groups, track cumulative counts, and identify which group contains the target position.

A visual pattern alternates colours with group sizes 1, 2, 3, 4, … (or a fixed cycle repeats). You find the colour or symbol at a large index such as the 30th bead.

Rule-based sequences make you apply the same if-then rule step after step — write each new number before moving on so you do not skip a transformation.

Even/odd divide-or-multiply chains appear in the medium band of Selective MR — one reliable mark when you track parity at every step.

The examiner tests whether you can apply conditional rules consistently (even → halve, odd → ×3+1) across several iterations without losing your place.

You start from a given whole number and apply a two-branch rule a fixed number of times (e.g. four steps). You report the final value.

Each child balances for half as long as the one before. Write out all five times first, then add carefully — convert to seconds to avoid decimal traps.

Halving (geometric) sequences appear regularly in Selective MR, often disguised as real-world scenarios (time, distance, money). The key skill is computing the sequence terms accurately and summing them without mistaking decimals for minutes and seconds.

The examiner tests whether students can apply a halving rule across 5 terms, convert 0.75 min to 45 seconds correctly (not 75 seconds), and add mixed minutes-and-seconds quantities. The most common error is treating 0.75 minutes as 75 seconds.

A sequence is defined by a starting value and a halving rule. Students must compute all terms and find their sum, expressing the answer in minutes and seconds.

The pattern goes 16, 20, 24, … — adding 4 each time. To count how many terms reach 404, use the nth-term formula: first + (n−1) × step = last. Solve for n.

Arithmetic sequence term-count questions appear regularly in the easy-to-medium band of Selective MR. Students who count up one-by-one from 16 will run out of time. The nth-term formula is the reliable shortcut.

The examiner tests whether students (1) identify the common difference (+4), (2) set up 16 + (n−1)×4 = 404, (3) correctly solve for n (n−1 = 97, so n = 98), and (4) avoid the off-by-one trap of answering 97 instead of 98.

An arithmetic sequence is defined by its first few terms and its last term. Students find how many terms are in the sequence.

Two alternating rules: −100 then +10, repeated. Work backwards from the 6th term by applying the inverse of each rule in reverse order.

Alternating-rule sequences appear in the medium-to-difficult band of Selective MR. Students who only apply one rule (e.g. just add 90 each step) will choose a wrong starting value. The key is tracking which rule applies at each position.

The examiner tests whether students (1) correctly alternate the two rules (not apply them once each), (2) work backwards by applying the inverse operations in reverse order, and (3) verify by running the sequence forward to check.

A sequence uses two alternating rules. A term part-way through is given. Students find the first term by working backwards.

Each number (from the 4th) = the three before it added together. Write equations for Y and the known term (6), solve for X, then find Z in one more step.

Tri-additive sequences with missing interior terms appear in the difficult band of Selective MR. Students who jump straight to Z without finding X and Y first always get stuck.

The examiner tests whether students can set up and solve two simultaneous equations using the tri-additive rule, working with both known and unknown positions in the sequence.

A sequence uses the rule ‘each term = sum of the three before it’. Some terms are given and some are labelled with letters. Students solve for the unknowns step by step.