document.write( "Question 767122: Really confused!! Help is greatly appreciated. My question is;\r
\n" ); document.write( "\n" ); document.write( "The number 4,375 is which term of the arithmetic sequence an = 3an-1, if a1 = 2.
\n" ); document.write( "a 7th term
\n" ); document.write( "b 8th term
\n" ); document.write( "c 9th term
\n" ); document.write( "d 6th term\r
\n" ); document.write( "\n" ); document.write( "In a, (n-1) is a lower exponent of a. and the 1 in a1 is another lower exponent to a. Its not above it like a normal exponent like 2^5, it's below it. please email me if you have any concerns! \n" ); document.write( "
Algebra.Com's Answer #467443 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "\r\n" );
document.write( "an = 3an-1, if a1 = 2. \r\n" );
document.write( "\r\n" );
document.write( "We check to see if it is a geometric sequence.\r\n" );
document.write( "\r\n" );
document.write( "r = \"a%5Bn%5D%2Fa%5Bn-1%5D\"\r\n" );
document.write( "\r\n" );
document.write( "Divide both sides of \r\n" );
document.write( "\r\n" );
document.write( "an = 3an-1 \r\n" );
document.write( "\r\n" );
document.write( "by an-1,\r\n" );
document.write( "\r\n" );
document.write( "\"a%5Bn%5D%2Fa%5Bn-1%5D\" = \"3a%5Bn-1%5D%2Fa%5Bn-1%5D\" = \"3cross%28a%5Bn-1%5D%29%2Fcross%28a%5Bn-1%5D%29\" = 3\r\n" );
document.write( "\r\n" );
document.write( "and since r = \"a%5Bn%5D%2Fa%5Bn-1%5D\", it is a geometric series with r = 3\r\n" );
document.write( "\r\n" );
document.write( "an = a1rn-1\r\n" );
document.write( "\r\n" );
document.write( "Substitute 4375 for an and 2 for a1\r\n" );
document.write( "\r\n" );
document.write( "4375 = 2(3n-1)\r\n" );
document.write( "\r\n" );
document.write( "Divide both sides by 2\r\n" );
document.write( "\r\n" );
document.write( "2187.5 = 3n-1\r\n" );
document.write( "\r\n" );
document.write( "Take logs of both sides\"\r\n" );
document.write( "\r\n" );
document.write( "log(2187.5) = log(3n-1)\r\n" );
document.write( "\r\n" );
document.write( "log(2187.5) = (n-1)log(3)\r\n" );
document.write( "\r\n" );
document.write( "\"log%28%282187.5%29%29%2Flog%28%283%29%29\" = n-1\r\n" );
document.write( "\r\n" );
document.write( "7.000208078 = n-1\r\n" );
document.write( "8.000208-78 = n\r\n" );
document.write( "\r\n" );
document.write( "That did not come out a whole number, \r\n" );
document.write( "so the problem is botched.  The 8th term is\r\n" );
document.write( "\r\n" );
document.write( "an = a1rn-1\r\n" );
document.write( "\r\n" );
document.write( "Substitute a1 = 2; n=8; r=3:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "a8 = 2·38-1\r\n" );
document.write( "\r\n" );
document.write( "a8 = 2·37\r\n" );
document.write( "\r\n" );
document.write( "a8 = 4374\r\n" );
document.write( "\r\n" );
document.write( "So you copied the problem wrong. \r\n" );
document.write( "It should have been 4,374,  not 4375.\r\n" );
document.write( "\r\n" );
document.write( "-----------------------------------------\r\n" );
document.write( "\r\n" );
document.write( "So change the problem from 4375 to 4374.\r\n" );
document.write( "\r\n" );
document.write( "an = a1rn-1\r\n" );
document.write( "\r\n" );
document.write( "Substitute 4374 for an and 2 for a1\r\n" );
document.write( "\r\n" );
document.write( "4374 = 2(3n-1)\r\n" );
document.write( "\r\n" );
document.write( "Divide both sides by 2\r\n" );
document.write( "\r\n" );
document.write( "2187 = 3n-1\r\n" );
document.write( "\r\n" );
document.write( "Take logs of both sides\"\r\n" );
document.write( "\r\n" );
document.write( "log(2187) = log(3n-1)\r\n" );
document.write( "\r\n" );
document.write( "log(2187) = (n-1)log(3)\r\n" );
document.write( "\r\n" );
document.write( "\"log%28%282187%29%29%2Flog%28%283%29%29\" = n-1\r\n" );
document.write( "\r\n" );
document.write( "7 = n-1\r\n" );
document.write( "8 = n\r\n" );
document.write( "\r\n" );
document.write( "So 4374 is the 8th term.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );