document.write( "Question 1162437: My co-worker got this exercise from somewhere regarding number sequences, and we can't figure it out.\r
\n" ); document.write( "\n" ); document.write( "6, 78, 85, 8, 17, 24, 10, 34, ??\r
\n" ); document.write( "\n" ); document.write( "We can't see a pattern and it feels like we've covered everything out there. \n" ); document.write( "

Algebra.Com's Answer #786247 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!
But greenestamps, this is the kind of problems they give you on tests to
\n" ); document.write( "get a job! It's true, because I remember many years ago when I was
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document.write( "6, 78, 85, 8, 17, 24, 10, 34\r\n" );
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document.write( "Obviously there is a pattern with term 1,4,7,10, \r\n" );
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document.write( "6,         8,         10,\r\n" );
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document.write( "So we know that the pattern goes:\r\n" );
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document.write( "6, 78, 85, 8, 17, 24, 10, 34, __, 12, __, __, 14\r\n" );
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document.write( "So we need a pattern for\r\n" );
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document.write( "   78, 85,    17, 24,     34, __,     __, __,\r\n" );
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document.write( "We notice that 85-78=7 and also 24-17=7\r\n" );
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document.write( "So term 3,6,9,12,15,... are 7 more than the terms just before them\r\n" );
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document.write( "So the number after 34 must be 7 more than 34, which is 41\r\n" );
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document.write( "So we have the next term, where your ?? is.  Is that all you want?\r\n" );
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document.write( "6, 78, 85, 8, 17, 24, 10, 34, 41\r\n" );
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document.write( "Or do you need to go further?  If so you'd need a pattern for\r\n" );
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document.write( "   78,        17,         34,        __,   \r\n" );
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document.write( "So the pattern is:\r\n" );
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document.write( "Terms 1,4,7,10,13 go 6,8,10,12,14,16,...\r\n" );
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document.write( "Terms 2,5,8,11,14 go 78,17,34,129,\r\n" );
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document.write( "which has the pattern:\r\n" );
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document.write( "1. Multiply the number of term by 13\r\n" );
document.write( "2. Subtract 152.\r\n" );
document.write( "3. Multiply by the number of term.\r\n" );
document.write( "4. Divide by 3\r\n" );
document.write( "5. Add 162\r\n" );
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document.write( "We get that the 2nd term is 78 by\r\n" );
document.write( "1. Multiplying 2 by 13, getting 26\r\n" );
document.write( "2. Subtracting 152, getting -126\r\n" );
document.write( "3. Multiplying by 2, getting -252\r\n" );
document.write( "4. Dividing by 3, getting -84\r\n" );
document.write( "5. Adding 162, getting 78, the 2nd term\r\n" );
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document.write( "We get that the 5th term is 17 by\r\n" );
document.write( "1. Multiplying 5 by 13, getting 65\r\n" );
document.write( "2. Subtracting 152, getting -87\r\n" );
document.write( "3. Multiplying by 5, getting -435\r\n" );
document.write( "4. Dividing by 3, getting -145\r\n" );
document.write( "5. Adding 162, getting 17, the 5th term\r\n" );
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document.write( "We get that the 8th term is 34 by\r\n" );
document.write( "1. Multiplying 8 by 13, getting 104\r\n" );
document.write( "2. Subtracting 152, getting -48\r\n" );
document.write( "3. Multiplying by 8, getting -384\r\n" );
document.write( "4. Dividing by 3, getting -128\r\n" );
document.write( "5. Adding 162, getting 34, the 8th term   \r\n" );
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document.write( "It's complicated, but it works.\r\n" );
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document.write( "Edwin

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