(a)

The brick staircase has bricks in the bottom step, hence .

There are steps in all, hence .

Each successive step requires two less bricks, hence .

Hence the sequence is .

Find the number of bricks in the top step.

The formula for  term: .

.

Therefore, bricks in the top step.

(b)

The sum of the first terms of an arithmetic sequence . \ \

.

Therefore, there are bricks to construct a brick staircase.

(a) There are bricks in the top step.

(b) There are bricks to construct a brick staircase.