A brick staircase has a total of 30 steps. The bottom step...

A brick staircase has a total of 30 steps. The bottom step requires 100 bricks. Each successive step requires two fewer bricks than the prior step.
(a) How many bricks are required for the top step?
(b) How many bricks are required to build the staircase?

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Arithmetic Series

An arithmetic series is the sum of the terms in an arithmetic sequence. The total number of bricks required for the staircase is found by summing the arithmetic series formed by the brick counts on each step. The sum can be calculated using the formula S_n = (n/2) * (first term + last term) or S_n = (n/2)[2a_1 + (n-1)d].

Nth Term Formula

The nth term formula for an arithmetic sequence allows you to calculate any term in the sequence using the first term and the common difference. It is given by a_n = a_1 + (n-1) * d, which is useful for determining quantities like the number of bricks on the top step of the staircase.

Common Difference

The common difference in an arithmetic sequence is the fixed amount by which the sequence increases or decreases from one term to the next. In the context of the staircase, it represents the consistent reduction in the number of bricks used from one step to the next.

Arithmetic Sequence

An arithmetic sequence is a list of numbers where each term after the first is created by adding (or subtracting) a constant value, known as the common difference, to the previous term. It is used to model situations where there is a regular increment or decrement, such as decreasing the number of bricks on each successive step.

Transcript

Please give Ace some feedback