Question 1196225: a gymnasium has 52 rows of seats. the last row contains 92 seats. if each row has 3 fewer seats tan the row behind it, how many seats are there in the first row?
Found 4 solutions by Alan3354, ikleyn, math_tutor2020, MathTherapy:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! a gymnasium has 52 rows of seats. the last row contains 92 seats. if each row has 3 fewer seats tan the row behind it, how many seats are there in the first row?
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92 - 3*52 = a negative number.
Answer by ikleyn(52782)  (Show Source):
You can put this solution on YOUR website! .
a gymnasium has 52 rows of seats. the last row contains 92 seats.
if each row has 3 fewer seats tan the row behind it, how many seats are there in the first row?
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The problem describes an IMPOSSIBLE situation, which never may happen.
The problem is FATALLY DEFECTIVE and is only good to throw it to the closest garbage bin.
It came from a  bad source.
Inform the source about this fatal deficiency.
Answer by math_tutor2020(3817)  (Show Source):
You can put this solution on YOUR website!
We have an arithmetic sequence because of the gap of 3 seats per row.
Counting down the sequence involves -3, so going up the sequence involves +3 or 3.
a = first term
d = 3 = common difference
first row = a
second row = a+3
third row = a+3+3 = a+3(2)
fourth row = a+3+3+3 = a+3(3)
fifth row = a + 3+3+3+3 = a + 3(4)
and so on
nth row = a+3(n-1)
We have n = 52 rows in total
That 52nd row has 92 seats
nth row = a+3(n-1)
52nd row = a+3(52-1)
92 = a+3(52-1)
92 = a+3(51)
a+3(51) = 92
a+153 = 92
a = 92-153
a = -61
The arithmetic sequence is: {-61, -58, -55, ..., 86, 89, 92} which consists of 52 terms
As you can see, we run into a problem. There's no way to have a negative number of seats in the first row. Or any row really.
Your teacher made a typo somewhere.
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! a gymnasium has 52 rows of seats. the last row contains 92 seats. if each row has 3 fewer seats tan the row behind it, how many seats are there in the first row?
If what you meant was that "each row has 3 fewer seats than the row behind in front of it,"
the AP would be:  , and the first row would have 245 seats.
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