A theater can seat 780 people. The number of rows is 4 less than the number of seats in each row. How many rows of seats are there

Answer 1

Using the sum of an arithmetic sequence with a=5 and d=4 we have to solve for n (which is the number of rows).
so...
780=(n/2)(2a+(n-1)4)
but we do the math and get down to
0=4n^2 +6n-1560 which needs the quadratic formula to factor. One of the roots of the quadratic formula is inadmissible (the negative one) and the other answer is approximately 19.01
Thus you can double check to see if you have 19 rows or 20 rows by subbing those numbers back into your sum formula where the sum = 780 : )

Answer 2

This is no sequence, since the rows all have the same number of seats. If there are n seats in each row, then there are n-4 rows, so

n(n-4) = 780
n = 30

There are 26 rows of 30 seats each

Answer 3

X seats/row.
x-4 Rows.

x*(x-4) = 780.
x^2 - 4x - 780 = 0,
Using Quadratic Formula,
X = 30.
x-4 = 26.