document.write( "Question 961086: the second term of a geometric progression is 36 more than the first term. the difference between the fourth and the third is 900. calculate the common ratio and the first term. \n" ); document.write( "
Algebra.Com's Answer #587377 by Edwin McCravy(20056)\"\" \"About 
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the second term of a geometric progression
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document.write( "\"a%5B2%5D=a%5B1%5Dr\"\r\n" );
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\n" ); document.write( "is 36 more than the first term.
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document.write( "\"a%5B2%5D=a%5B1%5D%2B36\"\r\n" );
document.write( "\"a%5B1%5Dr=a%5B1%5D%2B36\"\r\n" );
document.write( "\"a%5B1%5Dr-a%5B1%5D=36\"\r\n" );
document.write( "\"a%5B1%5D%28r-1%29=36\"\r\n" );
document.write( "\"a%5B1%5D=36%2F%28r-1%29\"\r\n" );
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\n" ); document.write( "the difference between the fourth and the third is 900.
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document.write( "\"a%5B4%5D-a%5B3%5D=900\"\r\n" );
document.write( "\"a%5B4%5D=a%5B1%5Dr%5E%284-1%29=a%5B1%5Dr%5E3\", \"a%5B3%5D=a%5B1%5Dr%5E%283-1%29=a%5B1%5Dr%5E2\"\r\n" );
document.write( "\"a%5B1%5Dr%5E3-a%5B1%5Dr%5E2=900\"\r\n" );
document.write( "\"a%5B1%5Dr%5E2%28r-1%29=900\"\r\n" );
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document.write( "Substitute \"a%5B1%5D=36%2F%28r-1%29\"\r\n" );
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document.write( "\"%2836%2F%28r-1%29%29r%5E2%28r-1%29=900\"\r\n" );
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document.write( "\"%2836%2Fcross%28r-1%29%29r%5E2%28cross%28r-1%29%29=900\"\r\n" );
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document.write( "\"36r%5E2=900\"\r\n" );
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document.write( "\"r%5E2=25\"\r\n" );
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document.write( "\"r+=+%22%22+%2B-+5\"\r\n" );
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document.write( "--------------------------\r\n" );
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document.write( "Using the positive value of r:\r\n" );
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document.write( "\"a%5B1%5D=36%2F%28r-1%29\"\r\n" );
document.write( "\"a%5B1%5D=36%2F%285-1%29\"\r\n" );
document.write( "\"a%5B1%5D=36%2F4\"\r\n" );
document.write( "\"a%5B1%5D=9\"\r\n" );
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document.write( "One solution r=5, a1=9\r\n" );
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document.write( "Checking:\r\n" );
document.write( "Sequence is 9,45,225,1125\r\n" );
document.write( "2nd term 45 is 36 more than 1st term 9.  9+36=45\r\n" );
document.write( "Difference between 4th and 3rd term is 1125-225=900 \r\n" );
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document.write( "Using the negative value of r:\r\n" );
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document.write( "\"a%5B1%5D=36%2F%28r-1%29\"\r\n" );
document.write( "\"a%5B1%5D=36%2F%28-5-1%29\"\r\n" );
document.write( "\"a%5B1%5D=36%2F%28-6%29\"\r\n" );
document.write( "\"a%5B1%5D=-6\"\r\n" );
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document.write( "Second solution r=-5, a1=-6\r\n" );
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document.write( "Checking:\r\n" );
document.write( "Sequence is -6,30,-150,750\r\n" );
document.write( "2nd term 30 is 36 more than 1st term -6.  -6+36=30\r\n" );
document.write( "Difference between 4th and 3rd term is 750-(-150)=750+150=900\r\n" );
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document.write( "-------------------------\r\n" );
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document.write( "Two solutions.\r\n" );
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document.write( "Edwin
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