document.write( "Question 1186524: A concert room has spaces for 10 seats in the first row, 13 in the second, 16 in the third, and so on.\r
\n" ); document.write( "\n" ); document.write( "a. If there are 20 rows in the theater, represent the total number of seats in the concert room in sigma notation.
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Algebra.Com's Answer #817442 by ikleyn(52793)\"\" \"About 
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\n" ); document.write( "A concert room has spaces for 10 seats in the first row, 13 in the second, 16 in the third, and so on.\r
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document.write( "(a)   The sequence is the arithmetic progression with the first term a = 10; the common difference d = 3\r\n" );
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document.write( "      and the number of terms n = 20.\r\n" );
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document.write( "      So, the formula for the n-th term of an arithmetic progression\r\n" );
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document.write( "          \"a%5Bn%5D\" = \"a%5B1%5D\" + (n-1)*d\r\n" );
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document.write( "      and it is the number of seats in the n-th row.\r\n" );
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document.write( "      The formula for the total number of seats is (sigma-notation)\r\n" );
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document.write( "          S = \"sum%28%2810+%2B+%28n-1%29%2A3%29%2C+n=1%2C20%29\".\r\n" );
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document.write( "(b)  To answer this question, apply the formula for the sum of n terms of an arithmetic progression\r\n" );
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document.write( "         \"S%5Bn%5D\" = \"%28a%5B1%5D+%2B+%28%28n-1%29%2Ad%29%2F2%29%2An\"\r\n" );
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document.write( "         \"S%5B20%5D\" = \"%2810+%2B+%28%2820-1%29%2A3%29%2F2%29%2A20\" = 770.\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( "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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