Some number sequences are organized by multiplication rather than addition. When values grow or shrink proportionally, comparing neighboring ratios can reveal a simpler pattern than comparing differences.
A constant ratio
Consider 64, 32, 16, 8. Each term is half the previous one, so the next term is 4. The differences vary, but the ratio stays at one-half.
For 2, 6, 18, 54, the common multiplier is three. The next value is 162. Check 6 ÷ 2, 18 ÷ 6 and 54 ÷ 18 before committing to the rule.
A changing multiplier
The sequence 2, 4, 12, 48 uses successive multipliers of two, three and four. Extending that multiplier pattern with five gives 240.
This is a different structure from a constant-ratio sequence. Naming it explicitly helps prevent applying ×4 again simply because that was the last operation.
Fractions can be part of a simple rule
For 81, 27, 9, 3, the next term is one, followed by one-third under the same divide-by-three rule. A sequence need not stop being regular when its terms cease to be whole numbers.
If a zero appears, division-based checks may be undefined. Use the full context rather than forcing every adjacent pair into a ratio. Negative terms can also signal sign alternation in addition to a multiplier.
Try a combined rule
In 1, 3, 7, 15, each term is double the previous value plus one. That rule predicts 31. It explains all three transitions, while a pure doubling rule does not.
Check the operation, then the arithmetic
Separate choosing a rule from calculating its next value. Once the rule fits, estimate the expected size and apply it carefully. A plausible pattern can still produce a wrong option through a multiplication error, so make the final arithmetic check part of your routine.