Question

Arithmetic Series:
each section of a soccer stadium has 44 rows with 22 seats in the first row, 23 in the second, 24 in the third and so on. how many seats are there
a) in row 44
b) in each section
c) in the stadium which has 25 sections?

Answer 1

first, how many seats in the last row? 22+43=65
then the sum could be done a couple ways.

(22+65)*44/2 = 1914 **

times 25 sections = 47850


one could also figure out how many seats in the average row, x number of rows.
since there are 44 rows, the average would be (row 22+row23) / 2 or
(43+44) / 2 = 87/2 =43.5 (notice 87 from the explanation below.)

43.5 * 44 = 1914

however, you really want to learn the formula.
once learned, it's easy and always works for an arithmetic simple series.

finally, when computing the last row length, it's first + number of rows-1.
eg, if there were only 3 rows, they'd have 22, 23, and 24.
24 = 22 + (3-1).
Source(s):
** the general formula for this type of series is,
(first + last) * number of entries / 2

the reason is, add first+last 22+65 = 87
then next to last -1 23+64 = 87
etc 24+63 = 87
and so on.
so how many 87's are there?
number of rows / 2