Nora created a tiled mosaic for display in her local art museum. The numbers of tiles in
the rows of the mosaic form an arithmetic sequence. The first row of the mosaic
has 8 tiles and the second row has 12 tiles.
a. Write an explicit formula representing this sequence.
b. Determine the number of tiles in the 13th row.
a. To find the explicit formula for this arithmetic sequence, we first need to identify the common difference between each row.
First row: 8 tiles
Second row: 12 tiles
12 - 8 = 4
The common difference is 4, so the explicit formula for the sequence is:
\( a_n = 8 + 4(n-1) \)
b. To find the number of tiles in the 13th row, we plug in n = 13 into the formula:
\( a_{13} = 8 + 4(13-1) \)
\( a_{13} = 8 + 4(12) \)
\( a_{13} = 8 + 48 \)
\( a_{13} = 56 \)
Therefore, there are 56 tiles in the 13th row.