SATHEE: Series Completion Tips

Series Completion Tips - Quick Revision

Prime Series: 2, 3, 5, 7, 11, 13… (next always +next-prime).
Square Series: 1, 4, 9, 16, 25… (difference rises by consecutive odd numbers).
Cube Series: 1, 8, 27, 64… (difference: 7, 19, 37… i.e. 2²–1, 3²–1, 4²–1).
Fibonacci: Every term = sum of previous two (1, 1, 2, 3, 5…).
Alternate Operation: +2, ×2, +3, ×3… (watch paired ops).
Pair-wise Skip: 2, 5, 3, 6, 4… (two interleaved APs).
Letter-series: Convert to A=1, B=2…; treat exactly like number series.
Three-tier diff: If 2nd difference is constant → quadratic; if 3rd difference constant → cubic.
Product-coded series: Each term = n × (n ± k); spot k.
Digit-sum series: 12, 15, 18, 21… (sum-of-digits increases by 3).
Reversal trick: 16, 61, 25, 52… (reverse digits alternately).
Missing-letter gap: Consecutive letters with gap 0,1,2,3… (a, c, f, k…).
Prime-gap rule: Gaps between primes themselves form primes (2→3 gap 1; 3→5 gap 2…).
Double-series: Even places follow ×3, odd places +4—solve separately.
Last-digit cycling: Powers of 2 end 2,4,8,6,2… every 4th repeats.

Formula/Rule	Application
nth term of AP: a + (n–1)d	Straight increasing/decreasing numbers
nth term of GP: arⁿ⁻¹	Multiply/divide by constant ratio
Sum of first n odd numbers = n²	Generates square series instantly
Difference of squares: (n+1)² – n² = 2n+1	Gap pattern in square series
Triangular numbers Tₙ = n(n+1)/2	1, 3, 6, 10… series
Prime-gap check: gap must leave primes on both ends	Validates suspected prime series
Letter-position mirror: A-Z (1-26), sum 27	Quick reverse-letter calc
Cyclicity of unit digit: 4 digits for 2/3/7/8; 2 for 4/9; 1 for 0/1/5/6	Predict last digit in power series
Quadratic fit: if 2nd diff constant, use an²+bn+c	Fit any 3 terms to find formula
Interleaved series: write odd & even positions on separate lines	Clarify mixed patterns

Mistake	Correct Approach
Ignoring alternate terms	Split odd/even positions first
Calculating 1st diff only	Go at least 3 levels deep for higher-order series
Treating 1 as prime	1 is NOT prime; start prime series from 2
Overlooking 0/negative terms	Include 0 in square/cube lists; check sign alternation
Forgetting letter wrap-around	After Z comes A (cycle 26) in circular letter series

First 5 sec: spot AP/GP; if not, split odd-even positions.
Write differences below series till constant; level count = degree of polynomial.
Keep 1-30 squares, 1-15 cubes, 1-50 primes memorised.
In letter Q, convert to numbers immediately; solve, then reconvert.
If two options fit, pick the simpler rule (Occam’s razor).

1. 3, 8, 15, 24, ?

35 (differences: 5,7,9,11)

2. 2, 3, 5, 9, 17, ?

33 (diff doubles: +1,+2,+4,+8,+16)

3. B, E, J, Q, ?

Z (positions: 2,5,10,17,26; gaps +3,+5,+7,+9)

4. 4, 16, 36, 64, ?

100 (even squares: 2²,4²,6²,8²,10²)

5. 1, 1, 2, 6, 24, ?

120 (factorial series: 1!,2!,3!,4!,5!,6!)