SOLUTION: an auditorium has 50 rows of seats. There are 8 seats in the first row, 10 seats in the second row, 12 seats in the third row, and so on. How many seats are in the auditorium

Algebra ->  Sequences-and-series -> SOLUTION: an auditorium has 50 rows of seats. There are 8 seats in the first row, 10 seats in the second row, 12 seats in the third row, and so on. How many seats are in the auditorium      Log On


   

Question 927495: an auditorium has 50 rows of seats. There are 8 seats in the first row, 10 seats in the second row, 12 seats in the third row, and so on. How many seats are in the auditorium
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
1st row: 8 + 0
2nd row: 8 + 2
3rd row: 8 + 4
4th row: 8 + 6
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The formula for adding up the numbers:
1 + 2 + 3 + 4 + 5 + . . . is:
+n%2A%28+n%2B1+%29+%2F+2+ where +n+
is the last number
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The 1st term in your sequence is:
+50%2A8+=+400+
The 2nd term in the sequence is:
2*( 1 + 2 + 3 + 4 + . . . + 49 )
+2%2A49%2A50+%2F+2+=+2450+
Note that the last term is +49+ because
the 1st term is +0+
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+400+%2B+2450+=+2850+
There are 2850 seats in the auditorium
Hope I got it -you might get a 2nd opinion, too