document.write( "Question 1145656: An amphitheater has a number of rows with 30 seats in the first row, 32 in the second, 34 in the third and so on.\r
\n" ); document.write( "\n" ); document.write( "The question is: How many rows should be there to get 3950 seats?
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\n" ); document.write( "I know that the formula to get the number of seats in a row is Sn(n/2)(a1+1n). But I'm struggling to figure out a formula to figure out how many rows there are given the number of seats.\r
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Algebra.Com's Answer #766885 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "It is arithmetic progression with the first term = 30,  the common difference d= 2  and the sum of the first n terms of 3950.\r\n" );
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document.write( "The formula for the sum of the first n terms is\r\n" );
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document.write( "     = \r\n" );
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document.write( "Substitute here   = 3950,   = 30  and d= 2. You will get\r\n" );
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document.write( "    3950 =  = 30n + n*(n-1) = n^2 +29n\r\n" );
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document.write( "    n^2 + 29n - 3950 = 0\r\n" );
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document.write( "    n =  =  = .\r\n" );
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document.write( "Only positive value is meaningful  n =  =  = 50.\r\n" );
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document.write( "ANSWER.  50 rows.    \r\n" );
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\n" ); document.write( "\n" ); document.write( "For introductory lessons on arithmetic progressions see \r
\n" ); document.write( "\n" ); document.write( "    - Arithmetic progressions\r
\n" ); document.write( "\n" ); document.write( "    - The proofs of the formulas for arithmetic progressions \r
\n" ); document.write( "\n" ); document.write( "    - Problems on arithmetic progressions \r
\n" ); document.write( "\n" ); document.write( "    - Word problems on arithmetic progressions\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Arithmetic progressions\".\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-II
\n" ); document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
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\n" ); document.write( "\n" ); document.write( "Comparing with the solution by @greenestamps, notice that I solved the problem algebraically
\n" ); document.write( "and presented THE METHOD to you, while he simply \"guessed\" the answer.\r
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\n" ); document.write( "\n" ); document.write( "The difference should be absolutely clear to you . . . \r
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