Series, Analogy and Coding-Decoding made clear.
Look for a rule that explains every supplied term. Start with simple changes and relationships, then test your candidate against the whole sequence rather than one convenient pair.
Key concepts in Series, Analogy and Coding-Decoding
Number series
Inspect differences, second differences, ratios, squares, cubes and alternating subsequences.
Analogy
Identify the relationship and its direction: tool:function differs from function:tool.
Letter positions
Use A=1 through Z=26 only when appropriate. Wrap after Z when the stated rule requires it.
Coding
Infer a consistent transformation from enough examples. A short sample can support more than one rule.
Find the differences
| Term | 3 | 7 | 13 | 21 | 31 | 43 |
|---|---|---|---|---|---|---|
| Change | +4 | +6 | +8 | +10 | +12 |
A reliable solving method
- Write the numbers or letter positions clearly.
- Try the simplest consistent rule before complex operations.
- Check every transition, including alternating positions.
- If several rules fit, use additional clues or answer choices rather than claiming a unique mathematical proof.
Step-by-step solved examples
Continue 3,7,13,21,31 under the consecutive-even-difference rule.
- Differences are 4,6,8,10.
- The next difference is 12.
- Next term = 31+12 = 43.
Bird:nest :: bee: ?
- The relation is animal to its dwelling.
- Apply the same relation to bee.
- Hive completes the analogy.
Every letter moves one step forward. Code CAT.
- C becomes D; A becomes B.
- T becomes U.
- The code is DBU.
Series, Analogy and Coding-Decoding: practice questions
Choose one answer before opening the explanation. Write down your reasoning as well as the option; a correct guess is different from a method you can repeat.
Using ×2 each step: 2,4,8,16, ?
Show answer and explanation — question 1
Answer D: 32
16×2 = 32.
Using consecutive squares: 1,4,9,16, ?
Show answer and explanation — question 2
Answer C: 25
The next square is 5² = 25.
Pen:write :: knife: ?
Show answer and explanation — question 3
Answer A: Cut
The relation is tool to its action.
Shift each letter +1. DOG becomes?
Show answer and explanation — question 4
Answer A: EPH
D→E, O→P, G→H.
Alternating sequences: 1,10,2,20,3,30, ?
Show answer and explanation — question 5
Answer A: 4
Odd positions are 1,2,3,4; even positions are 10,20,30.
A=1, Z=26. Position of M?
Show answer and explanation — question 6
Answer C: 13
M is the thirteenth letter.
Frequently asked questions
Should I always check differences first?
It is an efficient starting point, but multiplication or alternating patterns may fit better.
Can a code be uniquely decoded from one word?
Not always. Use all supplied examples and any explicitly stated coding rule.
Write the numbers or letter positions clearly. If several rules fit, use additional clues or answer choices rather than claiming a unique mathematical proof.