in the auditorium there are 24 rows of seats. the first second rows have 8 chairs and the third and fourth rows have 10 chairs.if this pattern continues.how many chairs are in the auditorium?
Since the rows come in pairs, the sequence looks like
8 8 10 10 12 12 ...
SO, considering the nth pair of rows, they have 12+4n seats together.
In 24 rows, there are 12 pairs, so
the 12th pair has 12+48 = 60 seats
the sum is
12/2 (8+60) = 6*68 = 408 seats
To determine the total number of chairs in the auditorium, we need to calculate the number of chairs in each row and then sum them up.
Based on the given pattern, we can observe that the number of chairs alternates between 8 and 10 for each pair of rows. The first and second rows have 8 chairs, while the third and fourth rows have 10 chairs. So we can break it down into sets of two rows.
Let's calculate the number of chairs for each set of two rows:
First set of two rows: 8 + 8 = 16 chairs
Second set of two rows: 10 + 10 = 20 chairs
From this, we can identify that for every set of two rows, the total number of chairs is 16 + 20 = 36 chairs.
Now, we need to find out how many sets of two rows are there in the auditorium. Since there are 24 rows in total, and each set consists of two rows, we can divide the total number of rows by 2 to get the number of sets:
Number of sets = 24 rows / 2 = 12 sets
Finally, to obtain the total number of chairs in the auditorium, we can multiply the number of sets by the number of chairs per set:
Total number of chairs = Number of sets * Number of chairs per set
Total number of chairs = 12 sets * 36 chairs per set
Total number of chairs = 432 chairs
Therefore, there are 432 chairs in the auditorium.