Question

Three friends agree to save money for a graduation road trip. They decide that each of them will put $0.25 in the fund on the first day of May, $0.50 on the second day, $0.75 on the third day, and so on. At the end of May, there will be $_____ in their fund. (Hint: There are 31 days in May.)

Answer 1

B{1} = .25(3)
B{2} = .50(3) + .25(3)
B{3} = .75(3) + .50(3)+ .25(3)

B{3} = 3(.75 + .50 + .25)

B{3} = 3(.25(3) + .25(2) + .25(1))

B{n} = 3(.25(n) + .25(n-1) + .25(n-2)+ ...+.25(2) +.25(1))

B{n} = 3(.25)((n) + (n-1) + (n-2)+ ...+(2) +(1))

just gotts determine a good function for the n parts now

Answer 2

A = { n + (n-1) + (n-2) + (n-3) +... + 2 + 1 }
+A = {1 + 2 + 3 + 4 + ...+ (n-1) + n }
--------------------------------------------
2A = {n+1 + n+1 + n+1 + n+1 + .... + n+1 + n+1}

2A = n(n+1)

n(n+1)
A = ------
2

Answer 3

B{n} = 3(.25)(A)

B{n} = .75(n)(n+1)/2 maybe :) lets try it out on day 1

B{1} = .75(1)(1+1)/2 = .75
B{2} = .75(2)(2+1)/2 = 2.25

i think it works :)

Answer 4

at day 31 they get:

.75(31)(32)/2 = 372