document.write( "Question 1040154: How many terms of the series 5+9+13+17... Must be added so that the sum will be 230? Please show the solution \n" ); document.write( "
Algebra.Com's Answer #654956 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "First we find the common difference by subtracting\r\n" );
document.write( "consecutive terms:\r\n" );
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document.write( "9-5=4\r\n" );
document.write( "13-9=4\r\n" );
document.write( "17-13=4\r\n" );
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document.write( "So the common difference d=4\r\n" );
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document.write( "Then we learn the formula for the sum of the first\r\n" );
document.write( "n terms:\r\n" );
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document.write( "\"S%5Bn%5D\"\"%22%22=%22%22\"\"expr%28n%2F2%29%28a%5B1%5D%2B%28n%2B1%29d%29\"\r\n" );
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document.write( "and learn what the terms mean:\r\n" );
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document.write( "n = the number of terms\r\n" );
document.write( "Sn = the sum of the first n terms\r\n" );
document.write( "a1 = the first term\r\n" );
document.write( "d = the common difference\r\n" );
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document.write( "We substitute Sn=230, a1=5, and d=4\r\n" );
document.write( "in \r\n" );
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document.write( "\"S%5Bn%5D\"\"%22%22=%22%22\"\"expr%28n%2F2%29%282a%5B1%5D%2B%28n-1%29d%29\"\r\n" );
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document.write( "and get\r\n" );
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document.write( "\"230\"\"%22%22=%22%22\"\"expr%28n%2F2%29%282%2A5%2B%28n-1%294%29\"\r\n" );
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document.write( "Multiply 2*5 and get 10\r\n" );
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document.write( "\"230\"\"%22%22=%22%22\"\"expr%28n%2F2%29%2810%2B%28n-1%294%29\"\r\n" );
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document.write( "Move the 4 in front of the (n-1)\r\n" );
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document.write( "\"230\"\"%22%22=%22%22\"\"expr%28n%2F2%29%2810%2B4%28n-1%29%29\"\r\n" );
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document.write( "Distribute the 4 into the (n-1)\r\n" );
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document.write( "\"230\"\"%22%22=%22%22\"\"expr%28n%2F2%29%2810%2B4n-4%29\"\r\n" );
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document.write( "Combine the 10 and the -4 getting 6 \r\n" );
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document.write( "\"230\"\"%22%22=%22%22\"\"expr%28n%2F2%29%286%2B4n%29\"\r\n" );
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document.write( "Clear the fraction by multiplying both sides by 2:\r\n" );
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document.write( "\"2%2A230\"\"%22%22=%22%22\"\"2%2Aexpr%28n%2F2%29%286%2B4n%29\"\r\n" );
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document.write( "Multiply the 2 times the 230 on the left getting 460.\r\n" );
document.write( "Cancel the 2's on the right:\r\n" );
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document.write( "\"460\"\"%22%22=%22%22\"\"cross%282%29%2Aexpr%28n%2Fcross%282%29%29%286%2B4n%29\"\r\n" );
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document.write( "Now we have:\r\n" );
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document.write( "\"460\"\"%22%22=%22%22\"\"n%286%2B4n%29\"\r\n" );
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document.write( "Can you solve that for n?  If not ask me how in the thank-you\r\n" );
document.write( "note form below and I'll get back to you by email.\r\n" );
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document.write( "Edwin
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