We can model this situation with an arithmetic series.
we have to find the number of all the seats, so we need to sum up the number of seats in all of the 22 rows.
1st row: 23
2nd row: 27
3rd row: 31
Notice how we are adding 4 each time.
So we have an arithmetic series with a first term of 23 and a common difference of 4.
We need to find the total number of seats. To do this, we use the formula for the sum of an arithmetic series (first n terms):
Sₙ = (n/2)(t₁ + tₙ)
where n is the term numbers, t₁ is the first term, tₙ is the nth term
We want to sum up to 22 terms, so we need to find the 22nd term
Formula for general term of an arithmetic sequence:
tₙ = t₁ + (n-1)d,
where t1 is the first term, n is the term number, d is the common difference. Since first term is 23 and common difference is 4, the general term for this situation is
tₙ = 23 + (n-1)(4)
The 22nd term, which is the 22nd row, is
t₂₂ = 23 + (22-1)(4) = 107
There are 107 seats in the 22nd row.
So we use the sum formula to find the total number of seats:
S₂₂ = (22/2)(23 + 107) = 1430 seats
Total of 1430 seats.
If all the seats are taken, then the total sale profit is
1430 * $29.99 = $42885.70
1. A geometric sequence has a common ratio. You can find the ratio by dividing every number by its previous one. If it is consistent, then the series is geometric.
a: 8/1=8, 27/8=3.375
b: (-3/2)/3=-1/2, (3/4)/(-3/2)=-1/2
c. 7/4=1.75, 10/7=1.429
d. 20/25=0.8, 14/20=0.7
Choice b is the only one that has a common ratio, so it is a geometric series.
2. Every term is multiplied by 1/3, so the common ratio is 1/3. d is the answer.
Answer:
10^8= 100,000,000
Step-by-step explanation:
10×10×10×10×10×10×10×10= 100,000,000
Answer:
5,000
Step-by-step explanation:
hope this is right
Answer:
x = 
y =
Step-by-step explanation:
the ratio of the sides of a 45 - 45 - 90 triangle is shown at the bottom of this answer.
as you can see, it is x:x:
The side given is x
, so you have:
divide both sides by
x = 
multiply this by 
y is also equal so y =
