Discovering Patterns in Nature, Daily Life, and Mathematics
Pattern Recognition
Welcome to the world of patterns!
Let's discover how mathematics appears everywhere around us
🌻 Patterns in Nature
🌻
Sunflower Petals
Petals follow mathematical sequences
Often in Fibonacci patterns
🍯
Honeycomb
Perfect hexagonal patterns
Uniform spacing and structure
🌽
Corn Kernels
Arranged in regular rows
Equal spacing between kernels
🪜 Ladder Pattern
45 cm
43 cm
41 cm
39 cm
37 cm
Each rung is 2 cm shorter than the one below
🏦 Shakila's Savings Plan
💰
Year 1
₹100
Year 2
₹150
Year 3
₹200
Year 4
₹250
Each year she adds ₹50 more than previous year
💼 Reena's Salary Progression
Year 1
₹8,000
Year 2
₹8,500
Year 3
₹9,000
Year 4
₹9,500
Annual increment of ₹500 each year
📚 What is an Arithmetic Progression?
An Arithmetic Progression (AP) is a sequence of numbers where each term is obtained by adding a fixed number to the previous term.
First term (a): The starting number of the sequence
Common difference (d): The fixed number added each time
🔢 General Form of AP
a, a+d, a+2d, a+3d, ...
Where: a = first term
d = common difference
Ready to explore patterns? Click any button below to begin!
Discover Pattern Recognition
🔍 Pattern Analysis
Patterns are everywhere around us! Arithmetic progressions help us understand and predict these regular sequences.
Click any button above to explore different types of patterns and learn how to identify them.
🎯 Practice: Identify the Patterns
Question 1: Which of these sequences forms an Arithmetic Progression?
2, 4, 8, 16, 32...
5, 8, 11, 14, 17...
1, 1, 2, 3, 5, 8...
3, 6, 12, 15, 18...
Question 2: In the sequence 7, 12, 17, 22, 27..., what is the common difference?
3
4
5
6
Question 3: If the first term is 10 and common difference is -3, what is the second term?