document.write( "Question 882717: Dear Sir/Madam;
\n" ); document.write( " A pleasant day! please help me with this sequence problem. Consider the sequence x+3, x+7, 4x-2...
\n" ); document.write( "a) if the sequence is arithmetic, find x and then determine the first 4 terms
\n" ); document.write( "b) if the sequence is geometric, find x and then determine the first 4 terms.\r
\n" ); document.write( "\n" ); document.write( "Thank you very much!
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Algebra.Com's Answer #533083 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
Consider the sequence x+3, x+7, 4x-2...
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\r\n" );
document.write( "a) if the sequence is arithmetic, then \r\n" );
document.write( "\r\n" );
document.write( "\"%28matrix%282%2C1%2Csecond%2C+term%29%29\"\"%22%22-%22%22\"\"%28matrix%282%2C1%2Cfirst%2Cterm%29%29\" \"%22%22=%22%22\" \"%28matrix%282%2C1%2Cthird%2C+term%29%29\"\"%22%22-%22%22\"\"%28matrix%282%2C1%2Csecond%2C+term%29%29\" \"%22%22=%22%22\" \"%28matrix%282%2C1%2Ccommon%2C+difference%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "     \r\n" );
document.write( "          \"x%2B7-x-3\"\"%22%22=%22%22\"\"4x-2-x-7\"\r\n" );
document.write( "                 \"4\"\"%22%22=%22%22\"\"3x-9\"      <-- so common difference = 4\r\n" );
document.write( "                \"13\"\"%22%22=%22%22\"\"3x\"\r\n" );
document.write( "                \"13%2F3\"\"%22%22=%22%22\"\"x\"\r\n" );
document.write( "\r\n" );
document.write( "first term = x+3 = \"13%2F3%2B3\" = \"13%2F3%2B9%2F3\" = \"22%2F3\"\r\n" );
document.write( "second term = \"22%2F3%2B4\" = \"22%2F3%2B12%2F3\" = \"34%2F3\"\r\n" );
document.write( "As a check,\r\n" );
document.write( "second term = x+7 = \"13%2F3%2B7\" = \"13%2F3%2B21%2F3\" = \"34%2F3\"\r\n" );
document.write( "third term = \"34%2F3%2B4\" = \"34%2F3%2B12%2F3\" = \"46%2F3\"\r\n" );
document.write( "As a check,\r\n" );
document.write( "third term = 4x-2 = \"4%2813%2F3%29-2\" = \"%2852%2F3%29-6%2F3\"= \"46%2F3\"\r\n" );
document.write( "fourth term = \"46%2F3%2B4\" = \"46%2F3%2B12%2F3\" = \"58%2F3\"\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "-------------\r\n" );
document.write( "\r\n" );
document.write( "b) if the sequence is geometric, then \r\n" );
document.write( "\r\n" );
document.write( "\"%28matrix%282%2C1%2Csecond%2C+term%29%29\"\"%22%F7%22\"\"%28matrix%282%2C1%2Cfirst%2Cterm%29%29\" \"%22%22=%22%22\" \"%28matrix%282%2C1%2Cthird%2C+term%29%29\"\"%22%F7%22\"\"%28matrix%282%2C1%2Csecond%2C+term%29%29\" \"%22%22=%22%22\" \"%28matrix%282%2C1%2Ccommon%2C+ratio%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "            \r\n" );
document.write( "\r\n" );
document.write( "        \r\n" );
document.write( "              \r\n" );
document.write( "        \"matrix%281%2C5%2Cx%5E2%2B14x%2B49%2C%22%22%2C%22%22=%22%22%2C%22%22%2C4x%5E2%2B10x-6%29\"\r\n" );
document.write( "\r\n" );
document.write( "        \"matrix%281%2C5%2C-3x%5E2%2B4x%2B55%2C%22%22%2C%22%22=%22%22%2C%22%22%2C0%29\"\r\n" );
document.write( "\r\n" );
document.write( "        \"matrix%281%2C5%2C3x%5E2-4x-55%2C%22%22%2C%22%22=%22%22%2C%22%22%2C0%29\"\r\n" );
document.write( "\r\n" );
document.write( "        \"matrix%281%2C5%2C%28x-5%29%283x%2B11%29%2C%22%22%2C%22%22=%22%22%2C%22%22%2C0%29\"\r\n" );
document.write( "\r\n" );
document.write( "Two solutions:\r\n" );
document.write( "       \r\n" );
document.write( "    \"matrix%281%2C5%2Cx-5%2C%22%22%2C%22%22=%22%22%2C%22%22%2C0%29\", \"matrix%281%2C5%2C3x%2B11%2C%22%22%2C%22%22=%22%22%2C%22%22%2C0%29\"\r\n" );
document.write( "\r\n" );
document.write( "      \"matrix%281%2C5%2Cx%2C%22%22%2C%22%22=%22%22%2C%22%22%2C5%29\",    \"matrix%281%2C5%2C3x%2C%22%22%2C%22%22=%22%22%2C%22%22%2C-11%29\"\r\n" );
document.write( "\r\n" );
document.write( "                    \"matrix%281%2C5%2Cx%2C%22%22%2C%22%22=%22%22%2C%22%22%2C-11%2F3%29\"\r\n" );
document.write( "\r\n" );
document.write( "Using x=5\r\n" );
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document.write( "first term = x+3 = \"5%2B3\" = \"8\"\r\n" );
document.write( "second term = x+7 = \"5%2B7\" = \"12\"\r\n" );
document.write( "common ratio = \"matrix%281%2C2%2Csecond%2Cterm%29%2Fmatrix%281%2C2%2Cfirst%2Cterm%29\" = \"12%2F8\" = \"3%2F2\"\r\n" );
document.write( "third term = \"12%2Aexpr%283%2F2%29\" = \"18\"\r\n" );
document.write( "As a check,\r\n" );
document.write( "third term = 4x-2 = \"4%285%29-2\" = \"20expr-2\" = \"18\"\r\n" );
document.write( "fourth term = \"18%2Aexpr%283%2F2%29\" = \"27\"\r\n" );
document.write( "\r\n" );
document.write( "Using x=\"-11%2F3\"\r\n" );
document.write( "\r\n" );
document.write( "first term = x+3 = \"-11%2F3%2B3\" = \"-11%2F3%2B9%2F3\" = \"-2%2F3\"\r\n" );
document.write( "second term = x+7 = \"-11%2F3%2B7\" = \"-11%2F3%2B21%2F3\" = \"10%2F3\"\r\n" );
document.write( "common ratio = \"matrix%281%2C2%2Csecond%2Cterm%29%2Fmatrix%281%2C2%2Cfirst%2Cterm%29\" = \"%28%2810%2F3%29%29%2F%28%28-2%2F3%29%29\" = \"%2810%2F3%29%28-3%2F2%29\"\"-5\"\r\n" );
document.write( "third term = \"%2810%2F3%29%28-5%29\" = \"-50%2F3\"\r\n" );
document.write( "As a check,\r\n" );
document.write( "third term = 4x-2 = \"4%28-11%2F3%29-2\" = \"%28-44%2F3%29-6%2F3\"= \"-50%2F3\"\r\n" );
document.write( "fourth term = \"%28-50%2F3%29%28-5%29\" = \"250%2F3\"\r\n" );
document.write( "\r\n" );
document.write( "Edwin
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