Answer:
A.) $2,166
B.) $10,545
C.) (n/2)(3.5 + 0.5n) × 38
Step-by-step explanation:
Floor - - - - - - - - - - 1 - - - - - - - 2 - - - - - - - 3
Cost / window - - $2.00 - - - $2.50 - - - $3.00
Cost of washing first floor = $2 × 38
Cost of second floor is: (2 + 0.5) × 38
Cost of third floor is: (2 + 2 × 0.5) × 38
Cost of n floor : (2 + (n - 1) × 0.5) × 38
Therefore,
Total cost :
(2 + (2 + 0.5) + (2 + 2*0.5) + ... + (2 + (n - 1)*0.5)) × 38
Using Arithmetic progression for the sequence :
2, (2 + 0.5), (2 + 2*0.5),..., (2 + (n - 1)*0.5)
first term 'a' = 2; common difference 'd' = 0.5
Sum of the first n terms of arithmetic sequence terms is:
S = (n/2)(2a + (n - 1)d) ; Where a = 2 and d = 0.5
S = (n/2)(2*2 + (n - 1)*0.5)
S = (n/2)(4 + 0.5n - 0.5)
S = (n/2)(3.5 + 0.5n)
To wash all windows with n stories :
S × 38 windows
A.) To wash all windows : stories = 12
n = 12
(12/2)(3.5 + 0.5(12)) × 38
6(3.5 + 6) × 38 = $2,166
B.) if building is 30 stories tall:
n = 30
(30/2)(3.5 + 0.5(30)) × 38
15(3.5 + 15) × 38 = $10,545
C.) If building is n stories tall :
(n/2)(3.5 + 0.5n) × 38
