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:
[tex]20+21=41[/tex]
And the information of the other 15 rows must be calculated: the third row has [tex]21+2=23[/tex], and the fourth [tex]23+2=25[/tex]. 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:
[tex]N=21+2n[/tex]
Her [tex]N[/tex] is the number of parking spaces and [tex]n[/tex] the number of row after the second row, in other words, [tex]n=1[/tex] is the third row. THe addition of the numbers of each row is:
[tex]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[/tex]
Using the formula:
[tex]\sum\limits^{n}_{i=1}i=\frac{n(n+1)}{2}[/tex]
[tex]T=356+2\sum\limits^{15}_{n=1}n\\T=356+2(\frac{15(15+1)}{2} )\\T=356+240\\T=596[/tex]
