Question

A brick staircase has 20 steps. The bottom step up has 80 bricks, the next step up has 78 bricks, the next step up has 76 bricks, and so on.
What explicit rule best represents the sequence 80,78,76,...?

Answer 1

Answer:

The explicit rule best represents the sequence 80,78,76,... is an = 78 + 2n

Step-by-step explanation:

Given Parameters.

Number of steps = 20

The bottom step = 80 bricks

The next step = 78 bricks,

The next step = 76 bricks,

Required:

What explicit rule best represents the sequence 80,78,76,...?

The topic in this question is arithmetic progression.

The nth term of a progression is solved using the formula

Tn = a + (n - 1)d

Where Tn represent the nth term

a = first term

n = number of terms

d = common difference

Comparing the above to the parameters in the question

a = first step = 80 bricks

n = number of steps =

d = common difference between 2 steps = 80 - 78 or 78 - 76

d = 2

Tn represents an

By Substituton, we have

an = 80 + (n - 1)2.

Open bracket

an = 80 + 2n - 2

Collect like terms

an = 80 - 2 + 2n

an = 78 + 2n

Hence, the explicit rule best represents the sequence 80,78,76,... is an = 78 + 2n

Answer 2

Answer:

aₙ = 82 - 2n

Step-by-step explanation:

aₙ = 82 - 2n