Question

A certain drive-in movie theater has a total of 17 rows of parking spaces. There are 20 parking spaces in the first row and 21 parking spaces in the second row. In each subsequent row there are 2 more parking spaces than in the previous row. What is the total number of parking spaces in the movie theater?

Answer 1

Answer:

596 parking spaces

Explanation:

The total of parking spaces is the sum of the parking spaces of each row, whit the 20 and 21 from the first and second row you have:

$20+21=41$

And the information of the other 15 rows must be calculated: the third row has $21+2=23$, and the fourth $23+2=25$. If we write the number of parking spaces in the fourth row in a way that the number 21 remains, we will have 21+4=25, and the 4 is the 2 added for each row multiplied by two rows so:

$N=21+2n$

Her $N$ is the number of parking spaces and $n$ the number of row after the second row, in other words, $n=1$ is the third row. THe addition of the numbers of each row is:

$T=20+21+21+2(1)+21+2(2)+...+21+2(15)\\T=20+21+\sum\limits^{15}_{n=1}(21+2n)\\T=41+\sum\limits^{15}_{n=1}21+\sum\limits^{15}_{n=1}2n\\T=41+21(15)+2\sum\limits^{15}_{n=1}n\\T=41+315+2\sum\limits^{15}_{n=1}n\\T=356+2\sum\limits^{15}_{n=1}n$

Using the formula:

$\sum\limits^{n}_{i=1}i=\frac{n(n+1)}{2}$

$T=356+2\sum\limits^{15}_{n=1}n\\T=356+2(\frac{15(15+1)}{2} )\\T=356+240\\T=596$