Homework Help: question

Posted by decker on Wednesday, January 21, 2009 at 10:00am.

bus holds 66 people. Starts out empty. Picks up 1 person at the 1st station. 2nd person at the 2nd station 3rd person at the 3rd station and so on. No one gets off. After how many stations will fill up the bus Show your work- explain your thinking?

question - bobpursley, Wednesday, January 21, 2009 at 10:06am
Wouldn't the last person get on at the 66th station?
question - Reiny, Wednesday, January 21, 2009 at 10:15am
the way you worded the question it simply becomes
1+1+1+1+... = 66
clearly 66 ones are needed, so after 66 stations the bus is full

if you meant 1st station one person gets one, on the 2nd station two people get on, on the third 3 people get on, etc
then it becomes a sequence/series type of question and you would have

1+2+3+4+... = 66
here a=1
d=1 and n is unknown but S(n) = 66
S(n) = n/2[2a + d(n-1)]
66 = n/2[2 + 1(n-1)]
132 = n[1+n]
n^2 + n - 132 = 0
(n+12)(n-11) = 0
n = -12 or n = 11
we need the positive integer solution which is 11
test: S(11) = 11/2[2 + 10] = 66

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