document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203513>Question 1203513</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A large multiplex movie house has many theaters.  The largest theater has 46 rows.  There are 16 seats in the first row.  Each row has two seats more than the previous row.  How many total seats are there in this​ theater? </SPAN>\n" );
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document.write( "Answer: <font color=red size=4>2806</font>\r<BR>\n" );
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document.write( "Work Shown\r<BR>\n" );
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document.write( "a1 = first term = 16<BR>\n" );
document.write( "d = common difference = 2<BR>\n" );
document.write( "Sn = sum of the first n terms of an arithmetic sequence<BR>\n" );
document.write( "Sn = (n/2)*(2*a1 + d*(n-1))<BR>\n" );
document.write( "Sn = (n/2)*(2*16 + 2*(n-1))<BR>\n" );
document.write( "S46 = (46/2)*(2*16 + 2*(46-1))<BR>\n" );
document.write( "S46 = <font color=red>2806</font>\r<BR>\n" );
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document.write( "Or we can compute the sum a slightly different way.<BR>\n" );
document.write( "an = nth term of arithmetic sequence<BR>\n" );
document.write( "an = a1 + d*(n-1)<BR>\n" );
document.write( "an = 16 + 2*(n-1)<BR>\n" );
document.write( "a46 = 16 + 2*(46-1)<BR>\n" );
document.write( "a46 = 106<BR>\n" );
document.write( "There are 106 seats in the 46th row.\r<BR>\n" );
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document.write( "Sn = sum of the first n terms of an arithmetic sequence<BR>\n" );
document.write( "Sn = (n/2)*(first term + nth term)<BR>\n" );
document.write( "Sn = (n/2)*(a1 + an)<BR>\n" );
document.write( "S46 = (46/2)*(a1 + a46)<BR>\n" );
document.write( "S46 = (46/2)*(16 + 106)<BR>\n" );
document.write( "S46 = <font color=red>2806</font>\r<BR>\n" );
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document.write( "The sum of the first 46 terms of the arithmetic sequence {16,18,20,22,...} is <font color=red>2806</font> which is the total number of seats in the theater room.\r<BR>\n" );
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document.write( "Spreadsheet software can be used to confirm the answer.<BR>\n" );
document.write( "Various online calculators are helpful as well.\r<BR>\n" );
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document.write( "A longer way to confirm the answer would be to compute the sum<BR>\n" );
document.write( "16+18+20+22+24+26+28+30+32+34+36+38+40+42+44+46+48+50+52+54+56+58+60+62+64+66+68+70+72+74+76+78+80+82+84+86+88+90+92+94+96+98+100+102+104+106 = 2806<BR>\n" );
document.write( "But it would be pointless busy-work to type all of that into a calculator.<BR>\n" );
document.write( "I do <u>not</u> recommend this confirmation method. Stick to the spreadsheet or other specialized calculators.<BR>\n" );
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