Question 3 - Relation of Shape Sequences to Number Sequences - Chapter 1 Class 6 - Patterns in Mathematics (Ganita Prakash)

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Question 3 How many little squares are there in each shape of the sequence of Stacked Squares? Which number sequence does this give? Can you explain why? Number of Little Squares in Each Shape: The sequence of Stacked Squares consists of square grids increasing in size: 1st shape: 1 × 1 grid → 1 square 2nd shape: 2 × 2 grid → 4 squares 3rd shape: 3 × 3 grid → 9 squares 4th shape: 4 × 4 grid → 16 squares 5th shape: 5 × 5 grid → 25 squares This forms the sequence: 1, 4, 9, 16, 25, 36, ... Which is square number sequence Explanation: Each shape is a square grid of size n x n, where n is the number of squares along one side. The total number of little squares in each shape is calculated by:​ Number of squares = 𝒏 × 𝒏=𝒏^𝟐 Therefore, the sequence represents the square numbers.