Verbal Reasoning · Sequence
Infer and apply one or two repeating symbolic rules.
Free to use and free to share. There is no sign-up, no score, and nothing a child does here is recorded or sent anywhere.
P, R, T, V … which tile rolls in next?
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One question of the kind this skill is tested with, worked all the way through: the reasoning, and what the wrong answers are there to catch.
Finding the rule a sequence follows
Which letter comes next in this sequence: T, M, F, Y, ...?
Work one sequence out and see how the rule is checked against every step, not just the first.
Answer: R
How you get there
Look at what happens from T to M: every step moves the letter back 7 places. Applying that to Y gives R. Check the same move works between every neighbouring pair before you use it, then take exactly one more step. The alphabet joins up at the end, so a step that runs back past A carries on again from Z.
Why the other answers tempt
The term the sequence has already reached, and the one after the answer, both feel like plausible next steps.
If they are stuck, say this
Work out the move between the first two terms, then check the same move gets you between every other pair.
P, R, T, V … which tile rolls in next?
A letter series is really a number series in disguise: swap each letter for its place in the alphabet and the pattern shows up. Here each letter jumps +2, every single step. Applying the jump once more to V gives X.
What to say if they get stuck
BD, FH, JL, N? - tap the letter on the strip that finishes the last pair.
Letter sequences are arithmetic in disguise, so turn the letters into positions before you do anything else: B is 2, D is 4, F is 6, H is 8, J is 10, L is 12, N is 14. Now two separate patterns appear. Inside every pair the second letter is two steps on from the first, and from one pair to the next every letter jumps four steps. The missing letter sits inside the last pair, so the rule you need is the plus two: N is 14, so the answer is 16, which is P. Always check both patterns before you answer, because these questions are built so that the between-pairs jump is a tempting wrong answer. Counting on the alphabet rather than guessing by feel is what keeps you right under time pressure.
What to say if they get stuck
34, 28, 22, 16, 10 … which carriage couples on the end?
Look at the couplings, not the carriages. The gaps between 34, 28, 22, 16, 10 are -6, -6, -6, -6 - and that is where the pattern lives: every coupling takes away 6. Carrying it on from 10 gives 4.
What to say if they get stuck
The frog can only land on a stone that carries on the pattern. Tap the lily pads to fill both blank stones.
This engine’s own main skill is Number Sequences. It practises continue a letter or number sequence alongside it.
The trap here is to spot the first gap and assume every gap is the same. From 3 to 6 the gap is 3, but from 6 to 12 the gap is 6, and from 12 to 24 it is 12. When the gaps themselves keep growing, stop adding and start looking for a multiplier: 3 times 2 is 6, 6 times 2 is 12, 12 times 2 is 24, so the sequence doubles and the next terms are 48 and 96. The general strategy for any sequence is to write the differences underneath first. Equal differences mean add the same number every time. Growing differences mean try multiplying, and if that fails try squares or a two-step rule such as double then add one.
What to say if they get stuck
The same exercise practises several skills, and telling them apart is often the difficulty rather than the exercise itself. On this page the skill is: infer and apply one or two repeating symbolic rules, and it stops where record rule count and alternation separately.
Infer and apply one arithmetic sequence rule. Excludes alternating rules and algebraic nth terms.
Use a stated or inferred linear rule to find a named term. One linear sequence only.
Translate between a letter and its ordinal alphabet position. One direct position, with direction stated.
Continue a code whose two explicit rules alternate. Exactly two repeating rules.
Answered from what the skill map records about this skill, not from a template. Every answer here is on the page, and the same questions are the page's FAQ structured data.
Infer and apply one or two repeating symbolic rules. It is one of 26 named verbal reasoning skills in the 11+, in the sequence strand, and this page carries 4 interactive exercises that practise it.
The term the sequence has already reached, and the one after the answer, both feel like plausible next steps. The wrong answers on this skill are built out of that, not out of random numbers, so it is worth naming out loud before your child meets it under time pressure.
Point at the next move rather than explaining the whole rule. Work out the move between the first two terms, then check the same move gets you between every other pair.
The skill map draws the line here: Record rule count and alternation separately. A question past that line is testing a different named verbal reasoning skill, which is worth knowing before you spend a week practising the wrong one.
Use Letter Conveyor, Alphabet Hops, Number Train and Frog Sequence Hop, embedded on this page. They are the exercises the skill map attaches to continue a letter or number sequence, they run in the browser with no account to make, nothing is scored, and nothing a child does here is recorded or sent anywhere. Each also has its own link, so you can send one to a child without sending them anywhere else first.
A free diagnostic works out which of the codes, analogies, word puzzles and logic types are already secure, and which are not.
