A brick wall is built by using 2 bricks less in each layer than in the previous one. The wall has m layers and in total 21m+40 bricks are used. If the top layer has only 4 bricks, determine:A) the value of m
b) the total number of bricks in the wall
i need to know how to do this one please
let a = 4
we know d = 2
Sm = m/2[8 + (m-1)(2)]
21m + 40 = m[3+m]
take over, (I got m=20)
Once you have m, sub into 21m+40 for the sum.
thx alot
To solve this problem, we need to create an equation based on the given information.
Let's assume that the number of bricks in the first layer is 'b'.
According to the given condition, in each subsequent layer, we use 2 fewer bricks than the previous one. Therefore, in the second layer, we use 'b - 2' bricks, in the third layer, we use 'b - 4' bricks, and so on.
Since the top layer has only 4 bricks, it must be the m-th layer. We can set up the following equation:
b + (b - 2) + (b - 4) + ... + 4 = 21m + 40
To simplify the equation, we can rewrite it as:
(b + 4) + (b + 2) + b + (b - 2) + (b - 4) + ... + 4 = 21m + 40
If we group the terms, we get:
m * b + (2 + 4 + ... + (b + 2) + (b + 4)) = 21m + 40
Simplifying further, we have:
m * b + (2 + 4 + ... + 2m) = 21m + 40
The sum of the first m even numbers (2 + 4 + ... + 2m) can be calculated using the formula:
Sum = m * (first term + last term) / 2
Plugging in the values, we get:
m * b + (m * (2 + 2m)) / 2 = 21m + 40
Simplifying, we have:
mb + m^2 + m = 21m + 40
Rearranging the terms, we get:
m^2 + (b + 1)m - 40 = 0
Now, we can solve this quadratic equation to find the value of m. Since we have a specific value for b (4), we can substitute it into the equation:
m^2 + (4 + 1)m - 40 = 0
Simplifying, we have:
m^2 + 5m - 40 = 0
Factoring the equation, we get:
(m + 8)(m - 5) = 0
So, the possible solutions are m = -8 and m = 5. However, the number of layers cannot be negative, so m = 5 is the valid solution.
Therefore, the value of m is 5.
To find the total number of bricks in the wall, we can substitute the value of m back into the equation:
b + (b - 2) + (b - 4) + ... + 4 = 21m + 40
Using b = 4 (as given in the question), the equation becomes:
4 + 2 + 0 + ... + 4 = 21 * 5 + 40
Simplifying, we get:
10 = 105 + 40
10 = 145
This is a contradiction, which means that the given values do not satisfy the problem conditions. There might be an error in the question or some missing information.