13. Number Series Pattern Recognition

Why This Chapter Matters

Series questions are short but time-sensitive. The skill is not advanced algebra; it is disciplined pattern checking.

Core Ideas

• Check first differences, second differences, multiplication/division, squares, cubes, and prime relationships.
• Some bank-exam series alternate between two mini-patterns.
• Series often use a mixed rule like multiply then subtract, or divide then add.
• If the numbers grow quickly, inspect the hidden base values instead of the visible terms alone.
• Odd-position and even-position subsequences often reveal the actual pattern.

High-Value Formulas

How To Approach Questions

1. Look for the simplest repeating operation first.
2. If one rule fails, test alternating positions separately.
3. Check difference tables before jumping to multiplication rules.
4. Check whether the terms come from squares, cubes, or primes.

Worked Examples

Example 1

Prompt: Find the next term in $12,21,59,231,1149,?$.

Approach: The pattern is $\times 1-?$, $\times 2-3$, $\times 3-4$, $\times 4-5$, $\times 5-6$. So next is $1149\times 6-7=6887$.

Example 2

Prompt: Find the next term in the cube sequence $12^3,14^3,16^3,18^3,20^3,?$.

Approach: The base numbers increase by $2$, so the next term is $22^3=10648$.

Example 3

Prompt: Find the next term in $4,9,16,25,?$.

Approach: These are consecutive squares: $2^2,3^2,4^2,5^2$. Next term is $6^2=36$.

Example 4

Prompt: Find the next term in $2,5,10,17,26,?$.

Approach: The differences are $3,5,7,9$. Next difference is $11$, so the next term is $37$.

Common Mistakes

• Jumping to a complex rule before checking easy differences.
• Ignoring alternating patterns.
• Missing the hidden square or cube base.
• Focusing on the answer choices before identifying the rule.

Quick Revision

Move from simple to complex: difference, multiplication, alternating rules, then special number sets.