document.write( "Question 736363: Is 12,40,68,96 sequence geometric or arthmetic? If possible what is the common ratio or difference
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Algebra.Com's Answer #449809 by MathLover1(20849)\"\" \"About 
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For \"arithmetic\" sequences, the common difference is \"d\", and the first term \"a%5B1%5D\" is often referred to simply as \"\"a\"\". Since you get the next term by adding the common difference, the value of \"a%5B2%5D\" is just \"a+%2B+d\". The third term is \"a%5B3%5D+=+%28a+%2B+d%29+%2B+d+=+a+%2B+2d\". The fourth term is \"a%5B4%5D+=+%28a+%2B+2d%29+%2B+d+=+a+%2B+3d\". Following this pattern, the \"n-th\" term an will have the form \r
\n" ); document.write( "\n" ); document.write( "\"a%5Bn%5D+=+a+%2B+d%28n+-1%29\".\r
\n" ); document.write( "\n" ); document.write( "For \"geometric\" sequences, the common ratio is \"r\", and the first term \"a%5B1%5D\" is often referred to simply as \"\"a\"\". Since you get the next term by multiplying by the common ratio, the value of \"a%5B2%5D\" is just \"ar\". The third term is \"a%5B3%5D+=+r%28ar%29+=+ar%5E2\". The fourth term is \"a%5B4%5D+=+r%28ar%5E2%29+=+ar%5E3\". Following this pattern, the \"n-th\" term an will have the form \r
\n" ); document.write( "\n" ); document.write( "\"a%5Bn%5D+=+ar%5E%28n+-1%29\".\r
\n" ); document.write( "\n" ); document.write( "in your case \"12\",\"40\",\"68\",\"96\" sequence is have the form \r
\n" ); document.write( "\n" ); document.write( "common difference is \"28\" and the greatest common divisor is \"4\"\r
\n" ); document.write( "\n" ); document.write( "first term is \"12\" and if divided by \"4\", we get \"3\" that could be written as \"7n-4\" starting with \"n=1\" and up
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\n" ); document.write( "so, the recursive formula is:\r
\n" ); document.write( "\n" ); document.write( "\"a%5Bn%5D=4%287n-4%29\"\r
\n" ); document.write( "\n" ); document.write( "and this is \"arithmetic\" sequence\r
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