A brick patio has the approximate shape of a trapezoid. The patio has 16 rows of bricks. The first row has a = 13 bricks and the 16th row has b = 28 bricks. How many bricks are in the patio?
Just blurting out an answer, especially if it is wrong, serves no purpose
sum = (n/2)(first + last)
= 8(13+28)
= 328
To find the total number of bricks in the patio, we need to find the sum of the number of bricks in each row.
We can apply the formula for the sum of an arithmetic series to solve this problem. The formula is:
S = (n/2) * (a + b)
Where:
S is the sum of the series
n is the number of terms in the series
a is the first term of the series
b is the last term of the series
In this case, the number of rows in the patio is n = 16, the number of bricks in the first row is a = 13, and the number of bricks in the 16th row is b = 28.
Substituting these values into the formula, we get:
S = (16/2) * (13 + 28)
S = 8 * (13 + 28)
S = 8 * 41
S = 328
Therefore, there are a total of 328 bricks in the patio.
To determine the total number of bricks in the patio, we need to find the sum of all the rows.
First, we need to find the total number of bricks in each row.
Given:
First row (a) = 13 bricks
Last row (b) = 28 bricks
Total number of rows (n) = 16 rows
We can find the total number of bricks in each row by using the formula for the sum of an arithmetic series:
Sn = (n / 2) * (a + b)
Substituting the given values:
S16 = (16 / 2) * (13 + 28)
Simplifying:
S16 = 8 * (13 + 28)
S16 = 8 * 41
S16 = 328
Therefore, there are a total of 328 bricks in the patio.