Using the expression $2n - 1$, can you find out how many tiles will be there in the $15^{\text{th}}$ stage and the $26^{\text{th}}$ stage of the pattern? Also, which stage will contain 21 tiles and 47 tiles?                                                                    [Page No. 22]

The rule for the number of tiles at Stage $n$ is $2n - 1$.

$15^{\text{th}}$ stage: $2 \times 15 - 1 = 29$ tiles.

$26^{\text{th}}$ stage: $2 \times 26 - 1 = 51$ tiles.

To find which stage has a given number of tiles, set $2n - 1$ equal to it and solve for $n$:

• 21 tiles: $2n - 1 = 21 \rightarrow 2n = 22 \rightarrow n = 11$.
Hence, Stage 11.

• 47 tiles: $2n - 1 = 47 \rightarrow 2n = 48 \rightarrow n = 24$.
Hence, Stage 24.