A number sequence gives you ordered values and asks for a missing or next term. The most useful first step is to inspect the relationships between neighboring values instead of guessing from the last number alone.
Start with differences
For 8, 13, 18, 23, subtract each term from the next. The differences are 5, 5 and 5, so the simple continuation is 28. Check all the steps; the same addition explains each one.
If the differences are not constant, inspect the differences themselves. For 2, 5, 10, 17, the increases are 3, 5 and 7. Continuing the odd increases with 9 gives 26.
Try ratios when growth is proportional
For 3, 9, 27, 81, consecutive terms have a ratio of three. The next term under that rule is 243. Adding a constant does not explain this sequence, while multiplication does.
Zero and negative values require care when dividing. Do not blindly compute a ratio through a zero term. Instead, look for an operation that remains defined and fits the entire sequence.
Check alternation before inventing a complicated formula
For 7, 14, 11, 22, 19, the operations alternate multiply by two and subtract three. The next term is 38. A single arithmetic operation is not enough, but a short repeating pair works.
A compact solving routine
- Calculate neighboring differences.
- Check simple ratios where appropriate.
- Inspect alternating operations or separate odd and even positions.
- Test the candidate rule against every displayed transition.
- Apply the rule once more and compare the available options.
Finite sequences admit many constructed continuations. In a reasoning question, prefer the simple consistent rule supported by the whole pattern and the options. During review, write the rule as an operation, not merely next comes 38. That makes the learning usable when the starting values change.