Measure the gaps
Subtract neighbouring terms. If the gaps change, inspect their gaps too. Regular differences can reveal a useful candidate rule.
OBSERVE / PROPOSE / EXPLAIN
A signal.
A possible rule.
Look beyond the next number. Test a pattern, follow the evidence and keep a note of what you noticed.
OBSERVATION 01
Awaiting signal
KNOWN OBSERVATIONSWHAT COULD COME NEXT?
THE INTENDED RULE
A finite sequence never proves a unique continuation.
Many rules can fit the same observations. We check against one deliberately chosen rule, then explain it. A different consistent rule may support a different answer.
THREE WAYS TO OBSERVE
Compare the scale
Try multiplication and division. Watch negative signs, and check every transition rather than just the first pair.
Separate the tracks
Odd and even positions may follow different rules. A short repeating block is another possibility worth testing.