Question 17 of 49intermediate🔧 ApplyNumerical2 marks

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?

Correct Answer

(15th stage) 29 tiles

(26th stage) 51 tiles

(Stage for 21 tiles) 11th stage

(Stage for 47 tiles) 24th stage

Exercise: Think and Reflect | Q: 1 | (Page 7)
For More Understanding

Explanation

The given expression for the number of tiles at Stage n is 2n - 1. To find the number of tiles for a specific stage, we substitute the stage number into the expression. Conversely, to find the stage number for a given number of tiles, we equate the expression to the number of tiles and solve for n.

Solution Steps

  1. Step 1: 15th stage calculation: Number of tiles = 2(15) - 1 = 30 - 1 = 29

  2. Step 2: 26th stage calculation: Number of tiles = 2(26) - 1 = 52 - 1 = 51

  3. Step 3: Stage for 21 tiles: 2n - 1 = 21 => 2n = 22 => n = 11. Thus, the 11th stage contains 21 tiles.

  4. Step 4: Stage for 47 tiles: 2n - 1 = 47 => 2n = 48 => n = 24. Thus, the 24th stage contains 47 tiles.

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