SOLUTION: I need your help with this problem: An ant farm can hold a total of 100,000 ants . If the farm held 1,500 ants the first day. 3,000 ants the second day, 6000 ants on the third d

Algebra ->  Equations -> SOLUTION: I need your help with this problem: An ant farm can hold a total of 100,000 ants . If the farm held 1,500 ants the first day. 3,000 ants the second day, 6000 ants on the third d      Log On


   

Question 326678: I need your help with this problem:
An ant farm can hold a total of 100,000 ants . If the farm held 1,500 ants the first day. 3,000 ants the second day, 6000 ants on the third day, and so on in this manner, in how many days will the farm be full?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
a1=1500
a2=3000
an=1500%2B1500%28n-1%29
Look at the sum of this arithmetic progression,
S=n%28a1%2Ban%29%2F2
S=n%281500%2B1500%28n-1%29%29%2F2
S=750n%281%2Bn-1%29
S=750n%5E2
Find n when S=100000
750n%5E2=100000
n%5E2=133.3
n=11.54
Between the 11th and 12th day, the farm will be full.