SOLUTION: An airplane climbs 100 feet during the first second after takeoff. In each succeeding second it climbs 100 feet more than it climbed during the previous second. How many seconds do

Algebra ->  Sequences-and-series -> SOLUTION: An airplane climbs 100 feet during the first second after takeoff. In each succeeding second it climbs 100 feet more than it climbed during the previous second. How many seconds do      Log On


   



Question 1034059: An airplane climbs 100 feet during the first second after takeoff. In each succeeding second it climbs 100 feet more than it climbed during the previous second. How many seconds does it take for the plane to reach an altitude of
12,000 feet above its takeoff height?
Answer 15 seconds (How?)

Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
Well, the situation describes the series
100 + 200 + 300 + 400 + ...where the total is the overall height of the airplane...we want to know when this total exceeds 12000...
Such an arithmetic series and sum can be described mathematically as
S%5Bn%5D+=+%28n%2F2%29%282a%5B1%5D+%2B+%28n-1%29d%29
Now plug in to get
12000+=+%28n%2F2%29%282%2A100+%2B+%28n-1%29%28100%29%29
12000+=+%28n%2F2%29%28200+%2B+100n+-+100%29
12000+=+%28n%2F2%29%28100n+%2B+100%29
Continue solving for n...
12000+=+50n%28n+%2B+1%29
240+=+n%28n%2B1%29
n%5E2+%2B+n+-+240+=+0
%28n%2B16%29%28n-15%29+=+0
n = 15