document.write( "Question 827422: I have to write a formula for a sequence of numbers whos tenth term is 75. Our teacher (a substitute) didn't really explain how to do this. Can you help me? \n" ); document.write( "
Algebra.Com's Answer #498722 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Use the 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( "with n=10  \r\n" );
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document.write( "a10 = a1 + (10-1)d\r\n" );
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document.write( "a10 = a1 + 9d\r\n" );
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document.write( "Substitute 75 for a10\r\n" );
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document.write( "75 = a1 + 9d\r\n" );
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document.write( "75 - a1 = 9d \r\n" );
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document.write( "Since the right side is 9d, pick a number for a1\r\n" );
document.write( "so that the left side will be a multiple of 9.  You don't\r\n" );
document.write( "have to, but that's the way to avoid fractions.  If we pick\r\n" );
document.write( "a1 to be 3, the left side will be 72 and that\r\n" );
document.write( "is divisible by 9.\r\n" );
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document.write( "So let's pick a1 = 3\r\n" );
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document.write( "75 - 3 = 9d\r\n" );
document.write( "    72 = 9d\r\n" );
document.write( "     8 = d\r\n" );
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document.write( "So substitute a1 = 3 and d = 8 in\r\n" );
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document.write( "an = a1 + (n-1)d\r\n" );
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document.write( "an = 3 + (n-1)(8)\r\n" );
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document.write( "an = 3 + 8n-8\r\n" );
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document.write( "an = 8n - 5     <-- answer\r\n" );
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document.write( "Then the sequence goes:\r\n" );
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document.write( "3,11,19,27,35,43,51,59,67,75,83,91,99,107,...\r\n" );
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document.write( "Notice that the tenth term is 75.\r\n" );
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document.write( "You could give other answers by choosing different \r\n" );
document.write( "numbers for a1.\r\n" );
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document.write( "Edwin
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