document.write( "Question 1128108: Consider the sequence that starts 1, -3, 6, -10, 15 of which 15 is the 5th term. if the 99th term of this sequence is 4950, what is the 100th term? \n" ); document.write( "
Algebra.Com's Answer #744609 by ikleyn(52788)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "2-nd term = -3 = 1 - 4 = \"1+-+2%5E2\"\r\n" );
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document.write( "3-rd term = 6 = -3 + 9 = \"-3+%2B+3%5E2\"\r\n" );
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document.write( "4-th term = -10 = 6 - 16 = \"6+-+4%5E2\"\r\n" );
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document.write( "5-th term = 15 = -10 + 25 = \"-10+%2B+5%5E2\".\r\n" );
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document.write( "The pattern is this recurrent formula  \"a%5Bn%2B1%5D\" = \"a%5Bn%5D+%2B+%28-1%29%5En%2A%28n%2B1%29%5E2\".\r\n" );
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document.write( "To find  \"a%5B100%5D\",  take  n+1 = 100 (hence n = 99)  and  \"a%5B99%5D\" = 4950  (as it is given).\r\n" );
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document.write( "Then you will get\r\n" );
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document.write( "\"a%5B100%5D\" = \"4950+%2B+%28-1%29%5E99%2A%2899%2B1%29%5E2\" = \"4950+%2B+%28-1%29%2A100%5E2\" = 4950 - 10000 = -5050.     ANSWER  \r\n" );
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\n" ); document.write( "\n" ); document.write( "My understanding is that not only an answer does matter - the solution (I mean the correct and correctly presented solution) does matter, too.\r
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\n" ); document.write( "\n" ); document.write( "It is why I wrote this post after the post by @Mtrkcrc.\r
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