document.write( "Question 749910: 1. The 100th Term is -354 the difference is -6 whats the first term?
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\n" ); document.write( "An=a1+d(n-10 and I dont understand Sn=n(a1+an)/2 \n" ); document.write( "
Algebra.Com's Answer #456216 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "It's all plugging numbers for letters in formulas.\r\n" );
document.write( "You just have to know what they mean.\r\n" );
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\n" ); document.write( "1. The 100th Term is -354
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document.write( "So n=100 and an = a100 = -354  \r\n" );
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\n" ); document.write( "2. the difference is -6
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document.write( "So d=-6\r\n" );
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\n" ); document.write( "3. whats the first term?
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document.write( "So a1 is what we're looking for\r\n" );
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document.write( "So we look through our storehouse of formulas \r\n" );
document.write( "for arithmetic sequences and series.\r\n" );
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document.write( "an = a1 + (n-1)d\r\n" );
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document.write( "Let's substitute 100 for n:\r\n" );
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document.write( "a100 = a1 + (100-1)d\r\n" );
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document.write( "Let's substitute -354 for a100:\r\n" );
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document.write( "-354 = a1 + (100-1)d\r\n" );
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document.write( "Let's substitute (-6) for d\r\n" );
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document.write( "-354 = a1 + (100-1)(-6)\r\n" );
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document.write( "Subtract 100-1\r\n" );
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document.write( "-354 = a1 + (99)(-6)\r\n" );
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document.write( "Multiply the 99 by the -6 and get -594\r\n" );
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document.write( "-354 = a1 - 594\r\n" );
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document.write( "Add 594 to both sides,\r\n" );
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document.write( "-354 = a1 - 594\r\n" );
document.write( "+594       +594  \r\n" );
document.write( "----------------\r\n" );
document.write( " 240 = a1\r\n" );
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document.write( "So the first term, a1, is 240.\r\n" );
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document.write( "---------------\r\n" );
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document.write( "To check it we write out all 100 terms, starting\r\n" );
document.write( "with 240 and adding -6 each time (same as \r\n" );
document.write( "subtracting 6) and see if when we get to the 100th number,\r\n" );
document.write( "it will be -354.  We'll make 10 rows and 10 columns going\r\n" );
document.write( "across:\r\n" );
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document.write( " 240  234  228  222  216  210  204  198  192  186\r\n" );
document.write( " 180  174  168  162  156  150  144  138  132  126\r\n" );
document.write( " 120  114  108  102   96   90   84   78   72   66\r\n" );
document.write( "  60   54   48   42   36   30   24   18   12    6\r\n" );
document.write( "   0   -6  -12  -18  -24  -30  -36  -42  -48  -54\r\n" );
document.write( " -60  -66  -72  -78  -84  -90  -96 -102 -108 -114\r\n" );
document.write( "-120 -126 -132 -138 -144 -150 -156 -162 -168 -174\r\n" );
document.write( "-180 -186 -192 -198 -204 -210 -216 -222 -228 -234\r\n" );
document.write( "-240 -246 -252 -258 -264 -270 -276 -282 -288 -294\r\n" );
document.write( "-300 -306 -312 -318 -324 -330 -336 -342 -348 -354\r\n" );
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document.write( "So we ended up with -354 as the 100th term in the \r\n" );
document.write( "lower right hand corner, so we know 240 was the \r\n" );
document.write( "correct first term a1.  But it does take a \r\n" );
document.write( "very long time to check them, so we just have to be\r\n" );
document.write( "careful with our calculations, and not check them.\r\n" );
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document.write( "-------------------------------------------------\r\n" );
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document.write( "The other formula you asked about:\r\n" );
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document.write( "Sn = \"n%2F2\"(a1 + an)\r\n" );
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document.write( " That is a formula for Sn, where S100 is the \r\n" );
document.write( "sum of all those 100 numbers if you were to add them all together:\r\n" );
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document.write( "There is another formula for the sum. It is:\r\n" );
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document.write( "Sn = \"n%2F2\"[2a1 + (n-1)d]\r\n" );
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document.write( "Edwin
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