The Dury Lane Theater has 15 seats in the first row and 40 rows in all. Each successive row contains one addition seat. How many seats are in the theater?

1 Answer
Alan P.
Jan 7, 2018

#1380# seats

Explanation:

Note that the last row will have #54# seats (see bottom of this explanation if why this is true is not clear).

#color(white)("2 times ")#total number of seats: #15+16+...+53+54#
#color(white)("2 times ")#total number of seats: #ul(54+53+...+16+15)#
2 times total number of seats:#" "underbrace(69+69+...+69+69)_(40" terms")#
#color(white)("xxxxxxxxxxxxxxxxxxxxxxxx")=69xx40=2760#

#rarr# total number of seats #=2760/2=1380#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Why does the last row have #54# seats?

If we number the rows from 1 to 40
then row 1 has #15=14+1# seats;
row 2 has #16=14+2# seats;
and so on, until
row 40 has #14+40=54# seats.

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