Answer:
Step-by-step explanation:
Since the 85 dollar fee is fixed, there should be no coefficient or constant that accompanies it. However, the total cost of the miles is directly proportional to the number of miles he drives. Thus, 0.35 should be accompanied by a constant that represents the total number of miles he drove. In this case, that constant is and
will represent the cost from the number of miles he drives in addition to the 85$ flat fee, hence
The chairs in the auditorium illustrates an arithmetic sequence
From the question, we have the following sequence:
Seats: 18, 26, 34
Rewrite as:
26 = 18 + 8
34 = 26 + 8
The above means that:
The number of seats on a row is 8 added to the the number of seats on the previous row.
Hence, the recursive rule is:
an = an-1 + 8; a1 = 26
<h3>The explicit rule</h3>In (a), we have:
a1 = 26 and d = 8
The explicit rule is calculated using:
an = a1 + (n -1) * d
This gives
an = 26 + (n - 1) * 8
Expand
an = 26 - 8 + 8n
Evaluate the difference
an = 18 + 8n
Hence, the explicit rule is:
an = 18 + 8n
<h3>The number of seats in the row 7</h3>This means that n = 7.
So, we have:
a7 = 18 + 8 * 7 = 74
Hence, there are 74 seats in the 7th row
<h3>The sigma notation</h3>We have the maximum number of rows to be 12.
So, the sigma notation would be:
The total number of seats is:
Sn = n/2(2a + (n -1) * d)
This gives
S12 = 12/2(2 * 26 + (12 -1) * 8)
S12 = 840
Hence, 840 chairs can fit the auditorium
Read more about arithmetic sequence at: