document.write( "Question 1139868: Find the sum of all even numbers from 4 to 100 inclusive, excluding those which are multiples of 3. \n" ); document.write( "
Algebra.Com's Answer #760373 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "            The  RIGHT  WAY  to solve the problem is  THIS :\r
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document.write( "            Calculate the sum of all even integers from 4 to 100 inclusively, and then subtract from it \r\n" );
document.write( "            the sum of all multiples of 6 from 6 to 96.\r\n" );
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\n" ); document.write( "\n" ); document.write( "            Below is how I implemented it.\r
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document.write( "(a)  the sum of all even integers from 4 to 100 inclusively is\r\n" );
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document.write( "         4 + 6 + 8 + . . . + 100 = \"%28%284+%2B+100%29%2F2%29%2A49\" = 2548.    \r\n" );
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document.write( "              (49 is the number of terms in this arithmetic progression).\r\n" );
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document.write( "(b)  the sum of all multiples of  6  from  6 to  96  inclusively is\r\n" );
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document.write( "         6 + 12 + 18 + . . . + 96 = \"%28%286+%2B+96%29%2F2%29%2A16\" = 816.    \r\n" );
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document.write( "              (16 is the number of terms in this arithmetic progression).\r\n" );
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document.write( "     In both cases (a) and (b), I applied the formula for the sum of the first \"n\" terms of an arithmetic progression.\r\n" );
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document.write( "(c)  The difference  2548 - 816 = 1732  is your  ANSWER.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Surely,  counting  \"by hands\"  (as the other tutor did)  is not the way to solve this problem.\r
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\n" ); document.write( "\n" ); document.write( "There is a bunch of lessons on arithmetic progressions in this site:\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( "    - One characteristic property of arithmetic progressions\r
\n" ); document.write( "\n" ); document.write( "    - Solved problems on arithmetic progressions \r
\n" ); document.write( "\n" ); document.write( "    - Mathematical induction and 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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