Question

Rayna is building a tapered staircase using bricks. The bottom stair is 45 bricks wide, and the top stair is 15 bricks ft wide. Each stair is 2 bricks shorter than the one below. What is the total amount of bricks Rayna needs to build the staircase? Type the total amount of bricks.

Answer 1

To find the total amount of bricks Rayna needs to build the tapered staircase, we can use the sum of arithmetic progression formula. By calculating the number of bricks for each stair using the given information, we find that Rayna needs 960 bricks in total.

Step-by-step explanation:

To find the total amount of bricks Rayna needs to build the staircase, we need to sum up the number of bricks for each stair. The bottom stair is 45 bricks wide, and the top stair is 15 bricks wide. Each stair is 2 bricks shorter than the one below. We can use arithmetic progression to calculate the number of bricks for each stair:

1. 
   
3. The first stair has 45 bricks.
4. 
   
6. The second stair has 45 - 2 = 43 bricks.
7. 
   
9. The third stair has 43 - 2 = 41 bricks.
10. 
    
12. And so on, until the top stair with 15 bricks.

To find the total amount of bricks, we can use the arithmetic progression formula:

Total number of bricks = (number of terms) * (first term + last term) / 2

Substituting the values into the formula:

Total number of bricks = ((45 - 15 + 2) * (45 + 15)) / 2 = (32 * 60) / 2 = 1920 / 2 = 960

Therefore, Rayna needs a total of 960 bricks to build the staircase.