Answer:
180 seats
Explanation:
You want the total number of seats in the first 8 rows of an auditorium in which the first row has 12 seats and each row after has 3 more than the previous row.
Seat count
The numbers of seats in the first 8 rows can be listed:
12, 15, 18, 21, 24, 27, 30, 33
Certainly, the sum can be found by adding up these numbers. Another way the sum can be found is by pairing the numbers symmetrically about the center of the list. Each of the 4 pairs totals 45:
12 +33 = 45
15 +30 = 45
18 +27 = 45
21 +24 = 45
Then the total is readily seen as 45×4 = 180.
The total number of seats in the first 8 rows is 180.
Formula
The sequence of seat counts is an arithmetic sequence with first term a1=12 and common difference d=3. The sum of n terms of such a sequence is given by the formula ...
Sn = (2·a1 +d(n-1))·(n/2)
For a1=12, d=3, n=8, this formula gives the total seat count as ...
S8 = (2·12 +3(8-1))·8/2 = (24 +21)(4) = 180