document.write( "Question 1181281: Determine the sum of all the two-digit multiples of 5.
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Algebra.Com's Answer #811150 by ikleyn(52908)\"\" \"About 
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document.write( "This sum is  \r\n" );
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document.write( "    S = 10 + 15 + 20 + 25 + . . . + 95.        (1)\r\n" );
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document.write( "Let's consider instead the sum\r\n" );
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document.write( "    T = 5 + 10 + 15 + 20 + 25 + . . . + 95.    (2)\r\n" );
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document.write( "The sum (2) is equal to  \r\n" );
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document.write( "    T = 5*(1 + 2 + 3 + 4 + 5 + . . . + 19)\r\n" );
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document.write( "It is well known fact that  1 + 2 + 3 + 4 + 5 + . . . + 19 = \"%2819%2A20%29%2F2\" = 19*10 = 190.  (the sum of the first n natural numbers).\r\n" );
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document.write( "So,  T = 5*190 = 950;  hence,  S = T - 5 = 950-5 = 945  and  can be computed mentally.\r\n" );
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document.write( "ANSWER.  The sum of all the two-digit multiples of 5 is  945.\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
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\n" ); document.write( "\n" ); document.write( "    - Word problems on arithmetic progressions\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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