find the number of seat in a theater
containing 30 rows if the first row has 14 seats and each row after that has 2 more seats than the previous row
14 + 16 + ... 70 + 72
Avg. number per row = (14+72)/2 = 43
Totsl = 43*30 = 1290.
To find the number of seats in a theater with 30 rows, where the first row has 14 seats and each subsequent row has 2 more seats than the previous row, you can use an arithmetic sequence formula.
The formula for finding the nth term of an arithmetic sequence is:
an = a1 + (n - 1)d
Where:
an is the nth term
a1 is the first term
n is the position of the term
d is the common difference between terms
In this case:
a1 = 14 (number of seats in the first row)
d = 2 (increase in the number of seats per row)
To find the number of seats in each row, we can use the formula for the 30th term (n = 30):
a30 = 14 + (30 - 1) * 2
Calculating this equation, we get:
a30 = 14 + 29 * 2
= 14 + 58
= 72
So, the number of seats in each row of the theater is 72.