Question 1 – Think & Reflect (Page 22) - Exploring Linear Patterns - Chapter 2 Class 9 - Introduction to Linear Polynomials (Ganita Manjari

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Question 1 – Think & Reflect (Page 22) Using the expression 2n – 1, can you find out how many tiles will be there in the 15th stage and the 26th stage of the pattern? Also, which stage will contain 21 tiles and 47 tiles? We found that Number of squares in Stage n = 2n – 1 Now, let’s answer our questions Number of tiles at 15th stage We put n = 15 in our formula Number of tiles at 15th stage = 2 × 15 – 1 = 30 – 1 = 29 Number of tiles at 26th stage We put n = 26 in our formula Number of tiles at 26th stage = 2 × 26 – 1 = 52 – 1 = 51 Now, the next part of our question is Which stage will contain 21 tiles? What about 47 tiles? Stage containing 21 tiles Here, we put Number of tiles = 21 and find n Now, Number of tiles = 2n – 1 21 = 2n – 1 21 + 1 = 2n 22 = 2n 2n = 22 n = 22/2 n = 11 So, at 11th stage we have 21 tiles Stage containing 47 tiles Here, we put Number of tiles = 47 and find n Now, Number of tiles = 2n – 1 47 = 2n – 1 47 + 1 = 2n 48 = 2n 2n = 48 n = 48/2 n = 24 So, at 24th stage we have 47 tiles