(a) row n has 25+(n-1)*1 = n+24 seats
so row 11 has 35 seats
(b) S32 = 32/2 (2*25 + 31*1)
The first row of a concert hall has 25 seats, and each row after the first has one more seat than the
row before it. There are 32 rows of seats. 35 students from a class want to sit in the same row.
a. In which row would the class sit?
b. How many seats are there in the concert hall?
2 answers
The number of seats in rows is an arithmetic progression.
For an arithmetic progression:
an = a + ( n - 1 ) d
where
a = the initial term
d = the common difference of successive members
an = the nth term
In this case:
a = 25 , d = 1
an = 25 + ( n - 1 ) ∙ 1
an = 25 + n - 1
an = 24 + n
a.
35 = 24 + n
Subtract 24 to both sides
35 - 24 = n
11 = n
n = 11
b.
Sum of the n terms of an AP:
S = n [ 2 a + ( n - 1 ) d ] / 2
In this case:
n = 32 , a = 25 , d = 1
S = n [ 2 a + ( n - 1 ) d ] / 2
S = 32 ∙ [ 2 ∙ 25 + ( 32 - 1 ) ∙ 1 ] / 2
S = 32 ∙ ( 50 + 31 ) / 2
S = 32 ∙ 81 / 2
S = 2592 / 2
S = 1296
For an arithmetic progression:
an = a + ( n - 1 ) d
where
a = the initial term
d = the common difference of successive members
an = the nth term
In this case:
a = 25 , d = 1
an = 25 + ( n - 1 ) ∙ 1
an = 25 + n - 1
an = 24 + n
a.
35 = 24 + n
Subtract 24 to both sides
35 - 24 = n
11 = n
n = 11
b.
Sum of the n terms of an AP:
S = n [ 2 a + ( n - 1 ) d ] / 2
In this case:
n = 32 , a = 25 , d = 1
S = n [ 2 a + ( n - 1 ) d ] / 2
S = 32 ∙ [ 2 ∙ 25 + ( 32 - 1 ) ∙ 1 ] / 2
S = 32 ∙ ( 50 + 31 ) / 2
S = 32 ∙ 81 / 2
S = 2592 / 2
S = 1296
5 answers