Number Series calculation

🔢 Number Series Calculation (Number Series) – Basics

A number series follows a certain pattern is a sequence of numbers. It is important to find missing number or next number.

📌 Definition

Numbers arranged in sequence following a certain ruleNumber Seriescalled

🧮 Common types

• ✔ Arithmetic Series (Addition / Subtraction)
• ✔ Geometric Series (Multiplication / Division)
• ✔ Square / Cube Series
• ✔ Mixed Pattern Series

🧮 Key Formulas

1️⃣ Arithmetic Series (AP)

a, a+d, a+2d, a+3d ...

nth term = a + (n-1)d

2️⃣ Geometric Series (GP)

a, ar, ar², ar³ ...

nth term = a × r^(n-1)

💡 Basic concept

• ✔ Check Difference (±)
• ✔ Check Ratio (× / ÷)
• ✔ Observe Squares / Cubes

📊 Example

2, 4, 6, 8, ?

Pattern = +2

Answer =10

📊 Example 2

3, 6, 12, 24, ?

Pattern = ×2

Answer =48

🔄 Key concepts

• ✔ Pattern finding is important
• ✔ Must be seen as Simple → Complex
• ✔ Can be two pattern mix

📏 Important notes

• ✔ AP and GP will be asked more
• ✔ Missing number questions common
• ✔ Practice will increase speed

Exams include “What is the next number?”, “Find the missing term”, Questions like “identify pattern” will be asked.

🔢 Number Series – Key formulas

🧮 1. Arithmetic Progression (AP)

a, a + d, a + 2d, a + 3d ...

nth term = a + (n - 1)d

• ✔ a = first number
• ✔ d = Common Difference

🧮 2. Geometric Progression (GP)

a, ar, ar², ar³ ...

nth term = a × r^(n - 1)

• ✔ r = Common Ratio

🧮 3. Sum of AP

S = n/2 [2a + (n - 1)d]

🧮 4. Sum of GP

S = a (r^n - 1) / (r - 1)

🧮 5. Square Series

1², 2², 3², 4² ...

🧮 6. Cube Series

1³, 2³, 3³, 4³ ...

🧮 7. Mixed Pattern

+, -, ×, ÷ combination

📏 Important notes

• ✔ AP → Difference (±)
• ✔ GP → Ratio (× / ÷)
• ✔ Observe Squares & Cubes
• ✔ Alternate pattern may exist

🔢 Number Sequence – 10 Examples + Shortcut Tricks

📘 Example 1

2, 4, 6, 8, ?

Trick:+2 patterns

Answer =10

📘 Example 2

5, 10, 20, 40, ?

Trick:×2 pattern

Answer =80

📘 Example 3

1, 4, 9, 16, ?

Trick:Squares (1², 2², 3²...)

Answer =25

📘 Example 4

1, 8, 27, 64, ?

Trick:Cubes (1³, 2³...)

Answer =125

📘 Example 5

3, 6, 9, 15, 24, ?

Trick:+3, +3, +6, +9 pattern

Answer =36

📘 Example 6

10, 20, 19, 38, 37, ?

Trick:×2, -1 alternate

Answer =74

📘 Example 7

2, 6, 7, 21, 22, ?

Trick:×3, +1 alternate

Answer =66

📘 Example 8

100, 90, 70, 40, ?

Trick:-10, -20, -30

Answer =0

📘 Example 9

1, 2, 6, 24, 120, ?

Trick:Factorial (n!)

Answer =720

📘 Example 10

4, 9, 19, 39, 79, ?

Trick:×2 +1 pattern

Answer =159

🚀 Key Shortcut Tricks

• ✔ Check Difference (±) first
• ✔ Next see Ratio (× / ÷).
• ✔ Remember Squares / Cubes
• ✔ Notice the alternate pattern
• ✔ Factorial pattern rare but important