Recursive Acceleration
The gap between consecutive terms keeps growing — or shrinking — by a fixed rule.
Recursive Acceleration is one of the most common pattern types in SHL Verify G+ and Cubiks Logiks Advanced assessments. Instead of adding the same number each step (simple arithmetic), the differences themselves follow a pattern: they may double, triple, or increase by a fixed amount. Candidates who only check first-level differences will miss it entirely. Mastering this pattern can unlock five or six correct answers in a standard assessment session.
How to solve it
- 1Write out the differences between consecutive terms: d₁ = t₂ − t₁, d₂ = t₃ − t₂, and so on.
- 2If those differences are not constant, compute the differences of the differences (second layer).
- 3If the second-layer differences are constant (e.g. all +2) or multiply by a fixed ratio (e.g. all ×2), you have Recursive Acceleration.
- 4To find the next term: extend the pattern to get the next difference, then add it to the last term.
- 5Watch for both growing sequences (differences increasing) and shrinking sequences (differences decreasing).
Worked examples
Example 1
Classic doubling differences
Rule: Each difference doubles
Example 2
Differences increasing by 1
Rule: Each difference increases by 1
Example 3
Downward acceleration (shrinking faster)
Rule: Each difference grows by −2
Common mistakes
- Stopping after the first layer of differences. If d₁, d₂, d₃... are not all the same, check whether they form a pattern of their own before giving up.
- Assuming the next difference equals the previous difference (i.e. treating it as arithmetic). Always verify that the second-layer is truly constant.
- Missing reversed sequences. A sequence like 64, 63, 61, 58, 54... decreases by growing gaps — still Recursive Acceleration.
Ready to practice?
Work through timed Recursive Acceleration questions and track your accuracy.