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