Atheater is set up so that there are 20 seats in the first row, and 4 additional seats in each consecutive row to the back of the theater where there are 144 seats. how many rows are there in the theater?

there are needed n=5.10 rows , but since it is not a round number (and for n=5 , S=140 ) , we could hypothesise that there are missing the additional 4 seats the first row , and the consecutive rows contains 4 additional seats than the first one , without counting the addition of 4 into the first row

Explanation:

Since the number of seats increases by 4 for every row , we have the formula

a(n+1) = a(n) + 4

therefore

a(n+1) - a(n) = 4 , summing  a(2) - a(1) ...

a(n) - a(1) = 4*(n-1)

a(n) = a(1) + 4*(n-1)

if in the first row a(1)=20

then the total number of rows S is obtained by summing all the a(n) for all the values of n (number of rows)

S= ∑ a(n) = ∑ [ a(1) + 4*(n-1) ] = ∑ [ (a(1)- 4) + 4*n ] = [a(1)-4]*n + 4*n*(n+1)/2

S= [a(1)-4]*n + 4*n*(n+1)/2 = [a(1)-4]*n + 2*n²+ 2*n = [a(1)-2]*n + 2*n²

thus

2*n² + [a(1)-2]*n - S = 0

replacing values a(1) = 20 seats , S=144 seats

2*n² + 18*n - 144 =0

n = [-18 + √(18² + 4*2*144)]/4 = 5.10

therefore n=5.10 rows are needed

since it is not a round number ( for n=5 , S=140 ) , we could hypothesise that there are missing the additional 4 seats the first row , and the consecutive rows contains 4 additional seats than the first one , without counting the addition of 4 into the first row

true

that is the way that they talked back then

=)

not because of any physical definition – as you can see cheerleading meets all of the athletic specifications. but, because cheerleading’s primary purpose is to support high school and college athletic teams. competition comes second! in other words, cheerleading is more than a sport.

explanation: