document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=69247>Question 69247</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have some answers but im not sure if they are right. I need this by tonight, can you please help me?\r<BR>\n" );
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document.write( "1) 	Use the arithmetic sequence of numbers 2, 4, 6, 8, 10… to find the following:<BR>\n" );
document.write( "a) 	What is d, the difference between any 2 terms? <BR>\n" );
document.write( "Answer: <BR>\n" );
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document.write( "b) 	Using the formula for the nth term of an arithmetic sequence, what is 101st term? Answer: <BR>\n" );
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document.write( "c) 	Using the formula for the sum of an arithmetic sequence, what is the sum of the first 20 terms? <BR>\n" );
document.write( "Answer:  430<BR>\n" );
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document.write( "You would add \r<BR>\n" );
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document.write( "d) 	Using the formula for the sum of an arithmetic sequence, what is the sum of the first 30 terms?<BR>\n" );
document.write( "Answer:  960\r<BR>\n" );
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document.write( "e) 	What observation can you make about the successive partial sums of this sequence (HINT: It would be beneficial to find a few more sums like the sum of the first 2, then the first 3, etc.)?<BR>\n" );
document.write( "Answer:  \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #49297 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=49297\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a)<BR>\n" );
document.write( "The distance is the factor between each term. So going from 2 to 4, 4 to 6, 6 to 8, you see that its adding 2 each time. To verify pick one term and subtract the previous term from it. So lets say I choose 8: I'm going to subtract 6 from it to get a difference of 2. If I pick 6, and subtract 4, I get a difference of 2.\r<BR>\n" );
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document.write( "So the distance (d) is\r<BR>\n" );
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document.write( "d=2\r<BR>\n" );
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document.write( "b)<BR>\n" );
document.write( "Using what we found earlier, I know that the sequence counts up by 2 each term. So if I'm at 8 (the 4th term) then my nth term is 4 (if we started at n=1). If I let n=5 then the term is 10. So if I divide 10 by 5 then I get 2, which means the term is doubled. This basically tells me that the arithmetic sequence is 2n. To verify, simply plug in the 1st term (n=1) and you'll get 2. Plug in the 2nd term (n=2) you'll get 4, etc. If I wanted to know the 101st term, let n=101 and it comes to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Ahighlight%28101%29=202 ALIGN=MIDDLE  ALT=\"2%2Ahighlight%28101%29=202\"   DISABLED_style= \"max-width:90%; height:auto;\" > So the 101st term is 202\r<BR>\n" );
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document.write( "c)<BR>\n" );
document.write( "Using the sum of arithmetic series formula:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=%28n%2F2%29%2A%28a%5B1%5D%2Ba%5Bn%5D%29 ALIGN=MIDDLE  ALT=\"s=%28n%2F2%29%2A%28a%5B1%5D%2Ba%5Bn%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > a[1]=first term, a[n]=nth term, and n is nth term<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=%2820%2F2%29%2A%282%2B40%29 ALIGN=MIDDLE  ALT=\"s=%2820%2F2%29%2A%282%2B40%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in values<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=%2810%29%2A%2842%29 ALIGN=MIDDLE  ALT=\"s=%2810%29%2A%2842%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >Simplify<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=420 ALIGN=MIDDLE  ALT=\"s=420\"   DISABLED_style= \"max-width:90%; height:auto;\" > So the sum of the first 20 terms is 420 (A minor discrepancy with your answer, I'd like to know what you did to get 430)\r<BR>\n" );
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document.write( "d)<BR>\n" );
document.write( "Again using the same formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=%28n%2F2%29%2A%28a%5B1%5D%2Ba%5Bn%5D%29 ALIGN=MIDDLE  ALT=\"s=%28n%2F2%29%2A%28a%5B1%5D%2Ba%5Bn%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > a[1]=first term, a[n]=nth term, and n is nth term<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=%2830%2F2%29%2A%282%2B60%29 ALIGN=MIDDLE  ALT=\"s=%2830%2F2%29%2A%282%2B60%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in values<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=%2815%29%2A%2862%29 ALIGN=MIDDLE  ALT=\"s=%2815%29%2A%2862%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >Simplify<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=930 ALIGN=MIDDLE  ALT=\"s=930\"   DISABLED_style= \"max-width:90%; height:auto;\" > close but no cigar, maybe you added the same term twice?\r<BR>\n" );
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document.write( "e)<BR>\n" );
document.write( "This one is a little tricky to explain, but the series (partial sums) follow the sequence <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2A%28n%2B1%29 ALIGN=MIDDLE  ALT=\"n%2A%28n%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (try it out by picking n=1,n=2,n=3,etc). To make a long story short, this sequence is the sum of n even integers.  </SPAN>\n" );
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