Alternating Operator
Two different operations take turns — odd steps follow one rule, even steps follow another.
Alternating Operator sequences catch many candidates off guard in SHL Verify G+ and Cubiks Logiks tests because the differences look completely random at first glance. The trick is recognising that there are two interleaved rules: one for odd-numbered steps (1→2, 3→4, 5→6…) and a different one for even-numbered steps (2→3, 4→5, 6→7…). Once you see the two-step cycle, the sequence becomes trivial.
How to solve it
- 1List the operations between consecutive terms: ×2, −3, ×2, −3... Look for a two-step repeating cycle.
- 2Check whether odd-positioned steps (1→2, 3→4, 5→6) all do the same thing.
- 3Check whether even-positioned steps (2→3, 4→5, 6→7) all do the same thing.
- 4Identify which position the missing term is in: the rule to apply depends on whether it follows an odd or even step.
- 5Common cycles: ×2 then −3, ÷2 then +5, ×3 then +3, +7 then ÷2.
Worked examples
Example 1
Multiply then subtract
Rule: Odd steps: ×2 · Even steps: −3
Example 2
Add then multiply
Rule: Odd steps: ×3 · Even steps: +3
Example 3
Two interleaved arithmetic sequences
Rule: Odd positions: +1 · Even positions: +2
Common mistakes
- Treating the sequence as a single sequence and computing differences across all terms. This produces values that seem random.
- Miscounting positions. Write out position numbers (1, 2, 3...) before identifying which step type applies to the answer.
- Confusing this with an Interleaved Sequence. Alternating Operator applies two different operations between terms; Interleaved Sequences are two independent sequences merged.
Ready to practice?
Work through timed Alternating Operator questions and track your accuracy.