document.write( "Question 1209375: Let a_1, a_2, a_3, ..., a_8, a_9, a_{10} be an arithmetic sequence. If a_1 + a_3 + a_5 = 5 and a_2 + a_4 = -2, then find a_1. \n" ); document.write( "

Algebra.Com's Answer #848702 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "Let a_1, a_2, a_3, ..., a_8, a_9, a_{10} be an arithmetic sequence. \r
\n" ); document.write( "\n" ); document.write( "If a_1 + a_3 + a_5 = 5 and a_2 + a_4 = -2, then find a_1.
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\n" ); document.write( "\n" ); document.write( " As this problem is posed in the post, it is FATALLY WRONG,\r
\n" ); document.write( "\n" ); document.write( " and I will explain below, WHY it is so.\r
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document.write( "If  the terms  a_1, a_2, a_3, a_4, a_5  form arithmetic sequence with the common difference d, \r\n" );
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document.write( "then the terms  a_1, a_3, a_5  also form arithmetic sequence, this time with the common difference 2d.\r\n" );
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document.write( "We can write these two equalities\r\n" );
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document.write( "    a_1 = a_3 - 2d,\r\n" );
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document.write( "    a_5 = a_3 + 2d.\r\n" );
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document.write( "By adding them, we get  a_1 + a_5 = 2a_3.\r\n" );
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document.write( "By adding a_3 to it, we get\r\n" );
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document.write( "    a_1 + a_3 + a_5 = 3a_3.\r\n" );
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document.write( "So,  3a_3 = 5 ,  and we get  a_3 = 5/3.\r\n" );
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document.write( "Similarly, we can write these two equalities\r\n" );
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document.write( "    a_2 = a_3 - d,\r\n" );
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document.write( "    a_4 = a_3 + d.\r\n" );
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document.write( "By adding them, we get\r\n" );
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document.write( "    a_2 + a_4 = 2a_3,\r\n" );
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document.write( "or\r\n" );
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document.write( "    2a_3 = -2,  a_3 = -2/2 = -1.\r\n" );
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document.write( "Thus we get for a_3 two different values, 5/3 and -1  simultaneously,   which is impossible and NEVER may happen.\r\n" );
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document.write( "So, we conclude that the problem is FATALLY INCONSISTENT.\r\n" );
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document.write( "It is SELF-CONTRADICTORY and describes a situation, which never may happen.\r\n" );
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\n" ); document.write( "\n" ); document.write( "From it, I make a conclusion, that a person, who created this \" problem \", is mathematically illiterate,\r
\n" ); document.write( "\n" ); document.write( "does not know the subject, produces HIBBERISH and disseminates it in the Internet, \r
\n" ); document.write( "\n" ); document.write( "confusing readers and making them to waste their precious time, which is REGRETTABLE. \r
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To the managers of this project

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\n" ); document.write( "\n" ); document.write( "As I explained in my post, a person, who created this \" problem \", is mathematically illiterate,\r
\n" ); document.write( "\n" ); document.write( "does not know the subject, produces HIBBERISH and disseminates it in the Internet, \r
\n" ); document.write( "\n" ); document.write( "confusing readers and making them to waste their precious time, which is REGRETTABLE. \r
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\n" ); document.write( "\n" ); document.write( " Please take the measures.\r
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