(-1,2) is where it will intersect
Answer:
a) -7/9
b) 16 / (n² + 15n + 56)
c) 1
Step-by-step explanation:
When n = 1, there is only one term in the series, so a₁ = s₁.
a₁ = (1 − 8) / (1 + 8)
a₁ = -7/9
The sum of the first n terms is equal to the sum of the first n−1 terms plus the nth term.
sₙ = sₙ₋₁ + aₙ
(n − 8) / (n + 8) = (n − 1 − 8) / (n − 1 + 8) + aₙ
(n − 8) / (n + 8) = (n − 9) / (n + 7) + aₙ
aₙ = (n − 8) / (n + 8) − (n − 9) / (n + 7)
If you wish, you can simplify by finding the common denominator.
aₙ = [(n − 8) (n + 7) − (n − 9) (n + 8)] / [(n + 8) (n + 7)]
aₙ = [n² − n − 56 − (n² − n − 72)] / (n² + 15n + 56)
aₙ = 16 / (n² + 15n + 56)
The infinite sum is:
∑₁°° aₙ = lim(n→∞) sₙ
∑₁°° aₙ = lim(n→∞) (n − 8) / (n + 8)
∑₁°° aₙ = 1
Answer:
Children ticket cost $30 and adult ticket costs $40.
Step-by-step explanation:
Given that:
x = price of a child ticket
y = price of an adult ticket
According to given statement;
3x+2y=170 Eqn 1
4x+6y=360 Eqn 2
Multiplying Eqn 1 by 3
3(3x+2y=170)
9x+6y=510 Eqn 3
Subtracting Eqn 2 from Eqn 3
(9x+6y)-(4x+6y)=510-360
9x+6y-4x-6y=150
5x=150
Dividing both sides by 5

Putting x=30 in Eqn 1
3(30)+2y=170
90+2y=170
2y = 170-90
2y = 80
Dividing both sides by 2

Hence,
Children ticket cost $30 and adult ticket costs $40.