Question

A soccer stadium has 25 sections of seating. Each section has 44 rows of seats, with 22 on the first row, 23 in the second row, 24 in the third row and so on. How many seats are there in:
row 44?
each section?
the whole stadium?

Answer 1

Answer:

A soccer stadium has 25 sections of seating.

Each section has 44 rows of seats, with 22 on the first row, 23 in the second row, 24 in the third row and so on.

A:

How many seats are there in row 44?

Arithmetic sequence is defined by

$a_n= a1 +d(n- 1)$

The common difference of the number of seats in each row is 1.

The first section has 22 seats.  

Therefore,

$a_n =22+(n -1)$

$a_n = n+21$

So, $a_44 = 44+21$

= 65 seats

B:

How many seats are there in each section?

We can add up these as the number of seats in one section = a1 + a2 + a3 + a4 +...... + a44

$Sum(44)= \frac{n}{2} (a+l)$

= $\frac{44}{2} (22+65)$

= 1914 seats

C:

How many seats are there in the whole stadium?

As there are 25 sections and each section as 1914 seats so, the whole stadium has $25\times1914=47850$ seats

= 47850 seats

Answer 2

Ok so it goes like this

i) It is an arithmetic progression
    a=22,d=1
Therefore Term 44= a + (n-1)d
                              =22+(44-1)1
                              =22+43
                              =65
So the answer is in row 44 there are 65 seats.

ii) Sum of 44 = n/2 (a+l)
                      =44/2 (22+65)
                      = 22 * 87
                      = 1914
So the answer is there are 1914 seats in a section.

iii) For the whole stadium= 1914*25
                                        = 47 850 seats