Question

A brick staircase has a total of 17 steps, with the first step requiring 118 bricks. Each successive step requires 5 less bricks than the prior one. How many bricks are required to build the staircase?

Answer 1

The answer is 1327.

Answer 2

1326 bricks

Explanation:

Step 1 will have 118 bricks

Step2 will be 118-5=113 bricks

Step 3 will have 118-(2*5)=108 bricks

Step 17 will have 118-(16*5)=38 bricks

The number of bricks in first step is given as 118+5(n-1) where n starts as 1

At any step n, the number of bricks will be 118+5(n-1)

The sum of the bricks can be found by

Sum=½n(n(1)+n(17))

Since n(1)=118 bricks and n(17) is 38 bricks

Sum=½*17(118+38)=1326 bricks