Using the expression 2n - 1 can you find out how many tiles will be there in the 15th stage Class 9

Using the expression 2n - 1 can you find out how many tiles will be there in the 15^th stage Class 9

Question 1.

Using the expression 2n - 1, can you find out how many tiles will be there in the 15^th stage and the 26^th stage of the pattern? Also, which stage will contain 21 tiles and 47 tiles? Class 9

Answer:

Number of tiles at stage n = 2n - 1

Substituting n = 15 in 2n - 1, we get

2(15) - 1 = 30 - 1 = 29

∴ There will be 29 tiles in the 15^th stage.

Substituting n = 26 in 2n - 1, we get

2(26) - 1= 52 - 1 = 51

∴ There will be 51 tiles in the 26^th stage.

For 21 tiles,

2n - 1 = 21

∴ 2n = 21 + 1= 22

∴ n = [latex]\frac{22}{2}[/latex]

∴ n = 11

∴ The 11^th stage will contain 21 tiles.

For 47 tiles,

2n - 1 = 47

∴ 2n = 47 + 1= 48

∴ n = [latex]\frac{48}{2}[/latex] = 24

∴ The 24^th stage will contain 47 tiles.