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# An amphitheater has 50 rows of seats with 30 seats in the

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VP
Joined: 14 May 2006
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An amphitheater has 50 rows of seats with 30 seats in the [#permalink]  11 Aug 2006, 14:01
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An amphitheater has 50 rows of seats with 30 seats in the first row, 32 in the second, 34 in the third, and so on. Find the total number of seats for all U2 fans for the upcoming U2 concert. (make sure to count u2lover in the 1st row )
Senior Manager
Joined: 07 Jul 2005
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Location: Sunnyvale, CA
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Re: PS: Amphitheater [#permalink]  11 Aug 2006, 14:15
u2lover wrote:
An amphitheater has 50 rows of seats with 30 seats in the first row, 32 in the second, 34 in the third, and so on. Find the total number of seats for all U2 fans for the upcoming U2 concert. (make sure to count u2lover in the 1st row )

This is an A.P. series
Sum of n terms = n/2(2a + (n-1)d)
= 50/2(2*30 + 49*2)
= 50*79
=3950
VP
Joined: 14 May 2006
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Re: PS: Amphitheater [#permalink]  11 Aug 2006, 14:26
sgrover wrote:
u2lover wrote:
An amphitheater has 50 rows of seats with 30 seats in the first row, 32 in the second, 34 in the third, and so on. Find the total number of seats for all U2 fans for the upcoming U2 concert. (make sure to count u2lover in the 1st row )

This is an A.P. series
Sum of n terms = n/2(2a + (n-1)d)
= 50/2(2*30 + 49*2)
= 50*79
=3950

what's d? and what's A.P. series? is the latter Arithm. progression?
Senior Manager
Joined: 07 Jul 2005
Posts: 404
Location: Sunnyvale, CA
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Re: PS: Amphitheater [#permalink]  11 Aug 2006, 14:44
u2lover wrote:
sgrover wrote:
u2lover wrote:
An amphitheater has 50 rows of seats with 30 seats in the first row, 32 in the second, 34 in the third, and so on. Find the total number of seats for all U2 fans for the upcoming U2 concert. (make sure to count u2lover in the 1st row )

This is an A.P. series
Sum of n terms = n/2(2a + (n-1)d)
= 50/2(2*30 + 49*2)
= 50*79
=3950

what's d? and what's A.P. series? is the latter Arithm. progression?

Yes. A.P. is the arithmetic progression
a - first term
n - #terms
d - difference between any two consecutive terms.

If first term is a, then nth term is: a + (n-1)d
Sum of n terms = n/2(2a + (n-1)d)

It can be easily derived.
(a1 + a2 .. + an)/n = mean
a1 + a2 .. +an = mean*n

In any A.P. mean of n terms = mean of first and last
mean = (a + a + (n-1)d)/2
= (2a+(n-1)d)/2

subsituting,
sum = n/2(2a+(n-1)d)
Current Student
Joined: 28 Dec 2004
Posts: 3387
Location: New York City
Schools: Wharton'11 HBS'12
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I am not sure if you can apply the progressive series here...

for instance say...

first row 30 seats
second row 32 seats
third row has 34 seats
well now if fourth row had 36 seats..Yes you can apply the progression series formula...

however if the 4th row had 38 seats..then you cant apply the progressive series...
VP
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Re: PS: Amphitheater [#permalink]  11 Aug 2006, 15:20
u2lover wrote:
An amphitheater has 50 rows of seats with 30 seats in the first row, 32 in the second, 34 in the third, and so on. Find the total number of seats for all U2 fans for the upcoming U2 concert. (make sure to count u2lover in the 1st row )

first row = 30
.
.
.
.
.
last row = 2 (50 - 1) + 30 = 128

so total = (50) (128 + 30)/(2) = 3950
Re: PS: Amphitheater   [#permalink] 11 Aug 2006, 15:20
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