Arithmetic Series

Question

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

 

a) row 44 of one section

 

b) each section

 

c) the whole stadium 

Answer 1

Arithmetic sequence is defined by

 

a_n = a₁ + d(n - 1)

 

where:

a_n = nth term

a₁ = first term

d = common difference between terms

n = term number

 

In this case,

 

n = nth row

a_n = # of seats

 

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

 

 

a)

 

a₄₄ = 44 + 21

     = 65

 

65 seats in the 44th row.

 

 

b)

 

If we add the number of seats starting from row 1 to row 44, we get the number of seats in each section.

 

number of seats in one section = a₁ + a₂ + a₃ + ...... + a₄₄

 

 

c)

 

number of seats in whole stadium = 25 * number of seats in one section