document.write( "Question 833482: Please help me with this sequence problem\r
\n" ); document.write( "\n" ); document.write( "Look at this sequence:7,12,17,22
\n" ); document.write( "What will the next three numbers be in the sequence? 27,32,37
\n" ); document.write( "Will 200 be in the sequence and how do you know? \n" ); document.write( "
Algebra.Com's Answer #502569 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "I'll show you another way below, but for illustrative purposes,\r\n" );
document.write( "here's one very slow and tedious way to find out (I used a computer\r\n" );
document.write( "program to list these, as I wouldn't have had the patience! :)\r\n" );
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document.write( "7, 12, 17, 22, 27, 32, 37, 42, 47, 52, 57, 62, 67, 72, 77, \r\n" );
document.write( "82, 87, 92, 97, 102, 107, 112, 117, 122, 127, 132, 137, 142,\r\n" );
document.write( "147, 152, 157, 162, 167, 172, 177, 182, 187, 192, 197, 202\r\n" );
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document.write( "As you see the answer is NO.  197 is a term and the next one\r\n" );
document.write( "is 202, skipping right over 200. But there is another way to find \r\n" );
document.write( "out without writing them out as the computer did in the list \r\n" );
document.write( "above.\r\n" );
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document.write( "One better way would be to reason out from the terms you found\r\n" );
document.write( " 7, 12, 17, 22, 27, 32, 37, that they must all either end in\r\n" );
document.write( "the digit 7 or 2, and since 200 does not end in either of\r\n" );
document.write( "those digits, it cannot be a term. \r\n" );
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document.write( "But the general way that will work in all cases is to use \r\n" );
document.write( "this formula for the nth term of an arithmetic sequence: \r\n" );
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document.write( "an = a1 + (n-1)d\r\n" );
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document.write( "The difference between terms is 5 so d=5.\r\n" );
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document.write( "a1 is the first term, which equals 7.\r\n" );
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document.write( "To see if 200 is a term in the sequence we assume\r\n" );
document.write( "that 200 is a term by substituting it in the formula \r\n" );
document.write( "above for the nth term an=200, and a1=7, d=5.\r\n" );
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document.write( "200 = (7) + (n-1)(5) \r\n" );
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document.write( "200 = 7 + 5(n-1)\r\n" );
document.write( "200 = 7 + 5n - 5\r\n" );
document.write( "200 = 2 + 5n\r\n" );
document.write( "198 = 5n\r\n" );
document.write( "\"198%2F5\" = n\r\n" );
document.write( "\"39%263%2F5\" = n\r\n" );
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document.write( "But n can only be a whole number, so we have reached a\r\n" );
document.write( "contradiction, and now we know that 200 will not be a\r\n" );
document.write( "term in the sequence.\r\n" );
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document.write( "Edwin
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