Competitive exam reasoning

Number Series Shortcuts for Competitive Exams

Most number-series questions become easier when you test patterns in a fixed order. Begin with differences, then ratios, alternating positions and familiar powers. This prevents overcomplicated guesses.

1

Check first and second differences

Subtract neighbouring terms. If the first differences are constant, continue them. If those differences change regularly, compare the differences again.

Solved exampleFor 2, 6, 12, 20, the gaps are 4, 6 and 8. The next gap is 10, so the next term is 30.
Common trapDo not name a pattern after checking only one transition.
2

Separate alternating positions

When adjacent terms appear unrelated, read the odd-position terms and even-position terms as two smaller series.

Solved exampleIn 2, 10, 4, 20, 6, 30, ?, the odd positions are 2, 4, 6, 8. The answer is 8.
Common trapConfirm whether the missing value belongs to the odd or even sequence.
3

Test ratios for rapid growth

Divide each term by the preceding term. A repeated ratio signals a geometric progression; changing ratios may reveal increasing multipliers.

Solved example3, 9, 27, 81 uses a ratio of 3, so the next value is 243.
Common trapRatios are not useful when the preceding term is zero.
4

Compare with squares and cubes

Values close to perfect squares or cubes often use a fixed addition or subtraction.

Solved example2, 5, 10, 17, 26 equals n² + 1 for n = 1 to 5. The next term is 37.
Common trapOne near-square is coincidence; verify the same offset across the sequence.
5

Repair a suspected wrong term

An incorrect middle value usually breaks the transition on both sides. Replace it with the value required by the simplest consistent rule, then recheck every step.

Solved exampleIn 3, 6, 12, 25, 48, doubling requires 24 instead of 25.
Common trapPrefer a simple rule that fits the complete series and the answer options.

Frequently asked questions

Which number-series pattern should I check first?

Check first differences first, followed by second differences, ratios, alternating positions and nearby squares or cubes.

How can I solve number series faster?

Write the gap or multiplier above each transition. A visible sequence of operations is quicker to verify and reduces mental-calculation errors.