Question 4 - Relation of Shape Sequences to Number Sequences - Chapter 1 Class 6 - Patterns in Mathematics (Ganita Prakash)

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Question 4 How many little triangles are there in each shape of the sequence of Stacked Triangles? Which number sequence does this give? Can you explain why? (Hint: In each shape in the sequence, how many triangles are there in each row?)Number of Little Triangles in Each Shape: 1st shape: 1 triangle 2nd shape: 1 (top row) + 3 (bottom row) = 4 triangles 3rd shape: 1 + 3 + 5 = 9 triangles 4th shape: 1 + 3 + 5 + 7 = 16 triangles 5th shape: 1 + 3 + 5 + 7 + 9 = 25 triangles This forms the sequence: 1, 4, 9, 16, 25, 36, ... Which is square number sequence Explanation: Each shape consists of rows of triangles, with the number of triangles in each row following the sequence of odd numbers: 1, 3, 5, 7, 9, 11, .. The total number of triangles in each shape is the sum of the first n odd numbers, which equals square of n. Total Triangles = 𝟏+𝟑+𝟓+…+(𝟐𝒏−𝟏)=𝒏^𝟐 Therefore, the sequence represents the square numbers. This forms the sequence: 1, 4, 9, 16, 25, 36, ... Which is square number sequence Explanation: Each shape consists of rows of triangles, with the number of triangles in each row following the sequence of odd numbers: 1, 3, 5, 7, 9, 11, .. The total number of triangles in each shape is the sum of the first n odd numbers, which equals square of n. Total Triangles = 𝟏+𝟑+𝟓+…+(𝟐𝒏−𝟏)=𝒏^𝟐 Therefore, the sequence represents the square numbers.