Final answer:
To calculate the total number of tiles in the artwork with 14 rows, where each row has one more tile than the previous, we use the formula for the sum of an arithmetic series and find the sum to be 105 tiles.
Step-by-step explanation:
The question involves finding the total number of tiles in a triangle-shaped tile artwork, where each subsequent row contains one more tile than the previous row. This forms an arithmetic sequence starting with 1 tile in the first row and increasing by 1 tile each row. To calculate the total number of tiles for 14 rows, we use the formula for the sum of an arithmetic series:
- Sum = n/2 × (first term + last term)
Where n is the number of terms, which in this case is 14 because there are 14 rows. The first term is 1 (the first row has 1 tile), and the last term is 14 (the 14th row has 14 tiles).
To find the sum, we replace the values into the formula:
Sum = 14/2 × (1 + 14)
Sum = 7 × 15
Sum = 105
Therefore, 105 tiles were used to make the artwork.