document.write( "Question 336715: a. 1, 3, 5, 7, 9
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Algebra.Com's Answer #241371 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "a. 1, 3, 5, 7, 9\r\n" );
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document.write( "That's an arithmetic sequence with first term \"a%5B1%5D=1\" and\r\n" );
document.write( "common difference \"d=2\", because you always ADD 2 to get the next term.\r\n" );
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document.write( "So we use \"a%5Bn%5D=a%5B1%5D%2B%28n-1%29%2Ad\"\r\n" );
document.write( "          \"a%5Bn%5D=1%2B%28n-1%29%2A2\"\r\n" );
document.write( "          \"a%5Bn%5D=1%2B2%28n-1%29\"   \r\n" );
document.write( "          \"a%5Bn%5D=1%2B2n-2\" \r\n" );
document.write( "          \"a%5Bn%5D=2n-1\"\r\n" );
document.write( "          \"a%5B100%5D\"\"%22%22=2%28100%29-1=200-1=199\"\r\n" );
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document.write( "b. 0, 50, 100, 150, 200\r\n" );
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document.write( "That's an arithmetic sequence with first term \"a%5B1%5D=0\" and \r\n" );
document.write( "common difference \"d=50\", because you always ADD 50 to get the next term.\r\n" );
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document.write( "That one is done exactly like problem a.  I'll let you do that one\r\n" );
document.write( "by yourself.\r\n" );
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document.write( "c. 3, 6, 12, 24, 48\r\n" );
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document.write( "That's a geometric sequence with first term \"a%5B1%5D=3\" and common\r\n" );
document.write( "ration \"r=2\", because you always MULTIPLY BY 2 to get the next term.\r\n" );
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document.write( "So we use \"a%5Bn%5D=a%5B1%5D%2Ar%5E%28n-1%29\"\r\n" );
document.write( "          \"a%5Bn%5D=3%2A2%5E%28n-1%29\"\r\n" );
document.write( "          \"a%5B100%5D\"\"%22%22=3%2A2%5E%28100-1%29=3%2A2%5E99\"\r\n" );
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document.write( "d. 10, 100, 1,000, 10,000, 100,000\r\n" );
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document.write( "That's a geometric sequence with first term \"a%5B1%5D=10\" and common \r\n" );
document.write( "ratio \"r=10\", because you always MULTIPLY BY 10 to get the next term.\r\n" );
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document.write( "That one is done exactly like problem c.  I'll let you do that one\r\n" );
document.write( "by yourself.\r\n" );
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document.write( "e. 9, 13, 17, 21, 25, 29\r\n" );
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document.write( "That's an arithmetic sequence with first term \"a%5B1%5D=9\" and \"d=4\",\r\n" );
document.write( "because you always ADD 4 to get the next term.\r\n" );
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document.write( "That one is done exactly like problem a.  I'll let you do that one\r\n" );
document.write( "by yourself.\r\n" );
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document.write( "f. 1, 8, 27, 64, 125 \r\n" );
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document.write( "Now that one is different from the others because it is neither an \r\n" );
document.write( "arithmetic sequence nor a geometric sequence.  However we can recognize it\r\n" );
document.write( "as the sequence of the cube of the successive positive integers.\r\n" );
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document.write( "1=1³, 8=2³, 27=3³, 64=4³, 125=5³\r\n" );
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document.write( "So \r\n" );
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document.write( "\"a%5Bn%5D=n%5E3\" \r\n" );
document.write( "\"a%5B100%5D\"\"%22%22=100%5E3=1000000\"\r\n" );
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document.write( "Edwin
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