document.write( "Question 322889: If the 3rd and 7th term of G.P are 81 and 16 respectively.Find the first 5th term of the G.P \n" ); document.write( "
Algebra.Com's Answer #231148 by Edwin McCravy(20086)\"\" \"About 
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document.write( "If the 3rd and 7th term of G.P are 81 and 16 respectively.\r\n" );
document.write( "Find the first 5th term of the G.P\r\n" );
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document.write( "\"a%5B1%5D\"\"%22=%22\"\"%22__%22\", \r\n" );
document.write( "\"a%5B2%5D\"\"%22=%22\"\"%22__%22\",\r\n" );
document.write( "\"a%5B3%5D\"\"%22=%22\"\"%2281%22\",\r\n" );
document.write( "\"a%5B4%5D\"\"%22=%22\"\"%22__%22\",\r\n" );
document.write( "\"a%5B5%5D\"\"%22=%22\"\"%22__%22\",\r\n" );
document.write( "\"a%5B6%5D\"\"%22=%22\"\"%22__%22\",\r\n" );
document.write( "\"a%5B7%5D\"\"%22=%22\"\"%2216%22\"\r\n" );
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document.write( "Look at the subsequence of b's:\r\n" );
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document.write( "\"b%5B1%5D\"\"%22%22=%22%22\"\"a%5B3%5D\"\"%22%22=%22%22\"\"%2281%22\",\r\n" );
document.write( "\"b%5B2%5D\"\"%22%22=%22%22\"\"a%5B4%5D\"\"%22%22=%22%22\"\"%22__%22\",\r\n" );
document.write( "\"b%5B3%5D\"\"%22%22=%22%22\"\"a%5B5%5D\"\"%22%22=%22%22\"\"%22__%22\",\r\n" );
document.write( "\"b%5B4%5D\"\"%22%22=%22%22\"\"a%5B6%5D\"\"%22%22=%22%22\"\"%22__%22\",\r\n" );
document.write( "\"b%5B5%5D\"\"%22%22=%22%22\"\"a%5B7%5D\"\"%22%22=%22%22\"\"%2216%22\"\r\n" );
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document.write( "We use the formula:\r\n" );
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document.write( "\"b%5Bn%5D\"\"%22%22=%22%22\"\"b%5B1%5D%2Ar%5E%28n-1%29\"\r\n" );
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document.write( "\"16\"\"%22%22=%22%22\"\"81%2Ar%5E%285-1%29\"\r\n" );
document.write( "\"16\"\"%22%22=%22%22\"\"81%2Ar%5E4\"\r\n" );
document.write( "\"16%2F81\"\"%22%22=%22%22\"\"r%5E4\"\r\n" );
document.write( "\"root%284%2C16%2F81%29\"\"%22%22=%22%22\"\"root%284%2Cr%5E4%29\"\r\n" );
document.write( "\"2%2F3\"\"%22%22=%22%22\"\"r\"\r\n" );
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document.write( "The common ratio r for the subsequence is the same\r\n" );
document.write( "as the common ratio for the original whole sequence.\r\n" );
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document.write( "So we multiply or divide by \"r=2%2F3\" as necessary to fill in\r\n" );
document.write( "the blanks:\r\n" );
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document.write( "To find \"a%5B2%5D\" we divide \"a%5B3%5D=81\" by \"r=2%2F3\":\r\n" );
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document.write( "\"81\"\"%22%F7%22\"\"2%2F3\"\"%22%22=%22%22\"\"81\"\"%22x%22\"\"3%2F2\"\"%22%22=%22%22\"\"243%2F2\"\r\n" );
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document.write( "To find \"a%5B1%5D\" we divide \"a%5B2%5D=243%2F2\" by \"r=2%2F3\":\r\n" );
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document.write( "\"243%2F2\"\"%22%F7%22\"\"2%2F3\"\"%22%22=%22%22\"\"243%2F2\"\"%22x%22\"\"3%2F2\"\"%22%22=%22%22\"\"729%2F4\"\r\n" );
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document.write( "To find \"a%5B4%5D\" we multiply \"a%5B3%5D=81\" by \"r=2%2F3\":\r\n" );
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document.write( "\"81\"\"%22x%22\"\"2%2F3\"\"%22%22=%22%22\"\"54\" \r\n" );
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document.write( "To find \"a%5B5%5D\" we multiply \"a%5B4%5D=54\" by \"r=2%2F3\":\r\n" );
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document.write( "\"54\"\"%22x%22\"\"2%2F3\"\"%22%22=%22%22\"\"36\" \r\n" );
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document.write( "To check we'll go ahead and find \"a%5B6%5D\"\r\n" );
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document.write( "We can find it either by multiplying \"a%5B5%5D\" by \"r=2%2F3\" \r\n" );
document.write( "or dividing \"a%5B7%5D\" by \"r=2%2F3\"\r\n" );
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document.write( "If we find a[6] by multiplying \"a%5B5%5D\" by \"r=2%2F3\" \r\n" );
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document.write( "\"36\"\"%22x%22\"\"2%2F3\"\"%22%22=%22%22\"\"24\" \r\n" );
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document.write( "If we find a[6] by dividing \"a%5B7%5D\" by \"r=2%2F3\" \r\n" );
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document.write( "\"36\"\"%22x%22\"\"2%2F3\"\"%22%22=%22%22\"\"24\" \r\n" );
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document.write( "\"16\"\"%22%F7%22\"\"2%2F3\"\"%22%22=%22%22\"\"16\"\"%22x%22\"\"3%2F2\"\"%22%22-%22%22\"\"24\"\r\n" );
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document.write( "So it checks.\r\n" );
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document.write( "Answers:\r\n" );
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document.write( "\"a%5B1%5D\"\"%22=%22\"\"%22729%2F4%22\", \r\n" );
document.write( "\"a%5B2%5D\"\"%22=%22\"\"%22243%2F2%22\",\r\n" );
document.write( "\"a%5B3%5D\"\"%22=%22\"\"%2281%22\",\r\n" );
document.write( "\"a%5B4%5D\"\"%22=%22\"\"%2254%22\",\r\n" );
document.write( "\"a%5B5%5D\"\"%22=%22\"\"%2236%22\",\r\n" );
document.write( "\"a%5B6%5D\"\"%22=%22\"\"%2224%22\",\r\n" );
document.write( "\"a%5B7%5D\"\"%22=%22\"\"%2216%22\"\r\n" );
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document.write( "Edwin
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