Question

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.

show all steps

Answer 1

Answer: Your welcome!

Explanation:

a. An explicit formula for this sequence is an = 8 + 4(n - 1), where n is the number of the row in the sequence.

b. To determine the number of tiles in the 13th row, we substitute 13 for n in the explicit formula:

an = 8 + 4(13 - 1)

an = 8 + 48

an = 56

Therefore, the 13th row of the mosaic has 56 tiles.

Thanks! :) #BO

Answer 2

a. an=4n + 4

b. 56 tiles

Explanation:

a. We know that the first term of the arithmetic sequence is 8 and the second term is 12. Let's call the common difference between consecutive terms "d". Then we can use the formula for the nth term of an arithmetic sequence:

an = a1 + (n - 1)d

where an is the nth term, a1 is the first term, and d is the common difference.

Using this formula, we can find the explicit formula for the sequence:

a1 = 8

a2 = 12

d = a2 - a1 = 12 - 8 = 4

Therefore, the explicit formula for the sequence is:

an = 8 + 4(n - 1) = 4n + 4

b. We need to find the number of tiles in the 13th row, which means we need to find a13. Using the explicit formula we just found:

a13 = 4(13) + 4 = 56

Therefore, there are 56 tiles in the 13th row of the mosaic.