Number Series

Before solving, look at the first and last number to decide the method.

• Slow Growth: (e.g., 5 to 50) $\to$ Check Difference (+/-).
• Fast Growth: (e.g., 5 to 5000) $\to$ Check Multiplication ($\times$).
• Super Fast Growth: $\to$ Check Squares/Cubes.
• Up-Down Pattern: $\to$ Check Alternating Series or $imes 0.5$ logic.

If a series decreases then increases (e.g., 10, 5, 5, 7.5...), it is ALWAYS a Decimal Multiplication series ($0.5$).

• Pattern: $\times 0.5, \times 1, \times 1.5, \times 2...$

If single difference fails, check the Difference of Difference. 90% of 'Unknown' logic questions are solved by Double Difference.

• Step 1: Find Diff 1.
• Step 2: Find Diff 2. Check for constant or AP pattern there.

Memorize Squares (1-30) and Cubes (1-15). Patterns often involve $n^2$ or $n^3$ with an offset.

• $n^2 + 1$: 2, 5, 10, 17...
• $n^3 - n$: 0, 6, 24, 60...
• $n^2 - n$: 0, 2, 6, 12...

Often confused with Odd numbers. If you see 2, 3, 5, 7... the next is NOT 9, it is 11.

• Prime Digits: The numbers themselves might be prime.
• Prime Addition: Gaps are prime numbers.

Two independent series hidden in one. Look for this when the length is long (7+ terms) or pattern goes Up-Down irregularly.

• Odd Positions: 1st, 3rd, 5th terms form a series.
• Even Positions: 2nd, 4th, 6th terms form another.

The hardest type. Don't find the next number; check which one BREAKS the rule.

• Rule: A wrong number usually affects two differences (the one before it and the one after it).
• Tip: Start from the end or the simplest part to establish the pattern first.