Unit 3 · Repeating Pattern Sequence
Study This Pattern — Find the Next Shape
Lesson 1 of 2
Welcome to one of the most satisfying question types in OC Thinking Skills — repeating sequences. Once you spot the cycle, finding any term in the sequence takes just a few seconds of arithmetic.
This exact format is a consistent presence on OC tests, and the technique is always the same whether the sequence is made of numbers, letters, or shapes. Many students gain a quick mark here by applying the method correctly.
The examiner wants to confirm that you understand a repeating sequence wraps around and that you can use division with remainder to locate any term without laboriously counting every single element up to that position.
A sequence that clearly repeats (e.g. 5, 6, 7, 8, 9, 5, 6, 7, 8, 9…) is shown, and you are asked to name the element at a large position — typically in the hundreds or thousands — where counting one by one would take too long.
Best approach: Count how many elements are in one full cycle. Divide the target position by the cycle length. The remainder tells you which position in the cycle your answer is at. Special case: if the remainder is 0, the answer is the LAST element of the cycle (not the first).
Question
Study this pattern. What is the 51st number?
5 6 7 8 9 5 6 7 8 9 5 6 ...
Select an answer to see the explanation.
Give Your Child the Best Chance at OC Entry
Join NSW families preparing their children for the Opportunity Class Placement Test with the most realistic online OC practice tests available. First tests free—no credit card required.
Claim Your Free OC Practice Tests