SOLUTION: A theater has 38 rows with 23 seats in the first row,26 in the second row,29 in the third row and so on. How many seats are in the theater?

Algebra ->  Sequences-and-series -> SOLUTION: A theater has 38 rows with 23 seats in the first row,26 in the second row,29 in the third row and so on. How many seats are in the theater?      Log On


   



Question 969329: A theater has 38 rows with 23 seats in the first row,26 in the second row,29 in the third row and so on. How many seats are in the theater?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The sequence is:
23, 26, 29, 32, . . . for 38 rows
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This is +20%2A38+=+760+ plus the sequence:
3, 6, 9, 12, . . . for 38 rows
This is:
+3n+ where +n+ is the row number , and
summed over the 38 rows
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This is +3+ times
+n+ row numbers summed over the 38 rows
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The formula for the summation is:
+%28+n%2A%28+n%2B1+%29+%29+%2F+2+=+%28+38%2A39+%29+%2F+2+
+%28+n%2A%28+n%2B1+%29+%29+%2F+2+=+1482+%2F+2+
+%28+n%2A%28+n%2B1+%29+%29+%2F+2+=+741+
+3%2A741+=+2223+
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+760+%2B+2223+=+2983+
There are 2,983 seats in the theater
hope I got it