document.write( "Question 100044: What is the formula for this sequences of numbers?
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Algebra.Com's Answer #72848 by Edwin McCravy(20060)\"\" \"About 
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What is the formula for this sequences of numbers?
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document.write( "First, check to see whether it is a geometric series, an \r\n" );
document.write( "arithmetic series or neither:\r\n" );
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document.write( "Checking to see if it is a geometric series:\r\n" );
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document.write( "Divide the 2nd term by the 1st term:  \"50%2F60\" = \"5%2F6\"\r\n" );
document.write( "Divide the 3rd term by the 2nd term:  \"40%2F50\" = \"4%2F5\"\r\n" );
document.write( "Divide the 4th term by the 3rd term:  \"30%2F40\" = \"3%2F4\"  \r\n" );
document.write( "Divide the 5th term by the 4th term:  \"20%2F30\" = \"2%2F3\"\r\n" );
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document.write( "These are certainly not all the same. In fact, they are all different.\r\n" );
document.write( "In fact, we could have stopped when we found that the 3rd term divided\r\n" );
document.write( "by the 2nd term was not the same as the 2nd term divided by the first\r\n" );
document.write( "term.\r\n" );
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document.write( "Therefore it is NOT a geometric series.\r\n" );
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document.write( "Checking to see if it is an arithmetic series:\r\n" );
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document.write( "Subtract: 2nd term minus 1st term:  \"50-60\" = \"-10\"\r\n" );
document.write( "Subtract: 3rd term minus 2nd term:  \"40-50\" = \"-10\"\r\n" );
document.write( "Subtract: 4th term minus 3rd term:  \"30-40\" = \"-10\"  \r\n" );
document.write( "Subtract: 5th term minus 4th term:  \"20-30\" = \"-10\"\r\n" );
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document.write( "These ARE all the same. \r\n" );
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document.write( "So it IS an arithmetic series, with common difference, d=-10\r\n" );
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document.write( "The formula for the nth term of an arithmetic sequence is\r\n" );
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document.write( "an = a1 + (n-1)d\r\n" );
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document.write( "where a1 = first term = 60 and d = common difference = -10\r\n" );
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document.write( "Substituting:\r\n" );
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document.write( "an = 60 + (n-1)(-10)\r\n" );
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document.write( "an = 60 + (-10)(n-1)\r\n" );
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document.write( "an = 60 - 10n + 10\r\n" );
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document.write( "an = 70 - 10n\r\n" );
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document.write( "That's it! Checking:\r\n" );
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document.write( "Plug in n=1 and you get a1 = 70 - 10(1) = 70-10 = 60 = the 1st term.\r\n" );
document.write( "Plug in n=2 and you get a2 = 70 - 10(2) = 70-20 = 50 = the 2nd term.\r\n" );
document.write( "Plug in n=3 and you get a3 = 70 - 10(3) = 70-30 = 40 = the 3rd term.\r\n" );
document.write( "Plug in n=4 and you get a4 = 70 - 10(4) = 70-40 = 30 = the 4th term.\r\n" );
document.write( "Plug in n=5 and you get a5 = 70 - 10(5) = 70-50 = 20 = the 5th term.\r\n" );
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document.write( "So it checks.\r\n" );
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document.write( "Edwin
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