document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1039313>Question 1039313</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Insert the indicated number of arithmetic means between the two given numbers \r<BR>\n" );
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document.write( "Three; a+2 and 5a-10 \r<BR>\n" );
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document.write( "So it looks like this \r<BR>\n" );
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document.write( "a+2 _ _ _ 5a-10\r<BR>\n" );
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document.write( "Find the three terms between them\r<BR>\n" );
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document.write( "Thank you please help me <BR>\n" );
document.write( "Please with solution so i can study it myself </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #654060 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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/cgi-bin/show-face.mpl?user=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=654060\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ONE WAY TO GET TO THE ANSWER (Probably the expected way):<BR>\n" );
document.write( "When you fill in the blanks, the five numbers (or expressions) form an arithmetic sequence.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=a%2B2 ALIGN=MIDDLE  ALT=\"a%5B1%5D=a%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the firs term of the sequence.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B5%5D=5a-10 ALIGN=MIDDLE  ALT=\"a%5B5%5D=5a-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the fifth element of the sequence.<BR>\n" );
document.write( "In an arithmetic sequence each term is the one before plus a common difference, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "In formulas, that is written as <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%2B1%5D=a%5Bn%5D%2Bd ALIGN=MIDDLE  ALT=\"a%5Bn%2B1%5D=a%5Bn%5D%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" > , or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=a%5Bn-1%5D%2Bd ALIGN=MIDDLE  ALT=\"a%5Bn%5D=a%5Bn-1%5D%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "As a consequence, any term is related to the first term, and the common difference by the formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D=a%5B1%5D%2B%28n-1%29%2Ad ALIGN=MIDDLE  ALT=\"a%5Bn%5D=a%5B1%5D%2B%28n-1%29%2Ad\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=5 ALIGN=MIDDLE  ALT=\"n=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B5%5D=a%5B1%5D%2B%285-1%29%2Ad ALIGN=MIDDLE  ALT=\"a%5B5%5D=a%5B1%5D%2B%285-1%29%2Ad\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B5%5D=a%5B1%5D%2B4d ALIGN=MIDDLE  ALT=\"a%5B5%5D=a%5B1%5D%2B4d\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since we know <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=a%2B2 ALIGN=MIDDLE  ALT=\"a%5B1%5D=a%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B5%5D=5a-10 ALIGN=MIDDLE  ALT=\"a%5B5%5D=5a-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > , we can substitute those expressions and solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" > :<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5a-10=a%2B2%2B4d ALIGN=MIDDLE  ALT=\"5a-10=a%2B2%2B4d\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5a-10-a-2=a%2B2-a-2%2B4d ALIGN=MIDDLE  ALT=\"5a-10-a-2=a%2B2-a-2%2B4d\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4a-12=4d ALIGN=MIDDLE  ALT=\"4a-12=4d\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284a-12%29%2F4=d ALIGN=MIDDLE  ALT=\"%284a-12%29%2F4=d\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=a-3 ALIGN=MIDDLE  ALT=\"d=a-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Now, we can find the missing terms:<BR>\n" );
document.write( "The second term is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B2%5D=a%5B1%5D%2Bd=a%2B2%2Ba-3=highlight%282a-1%29 ALIGN=MIDDLE  ALT=\"a%5B2%5D=a%5B1%5D%2Bd=a%2B2%2Ba-3=highlight%282a-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The third term is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B3%5D=a%5B2%5D%2Bd=2a-1%2Ba-3=highlight%283a-4%29 ALIGN=MIDDLE  ALT=\"a%5B3%5D=a%5B2%5D%2Bd=2a-1%2Ba-3=highlight%283a-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The fourth term is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B4%5D=a%5B3%5D%2Bd=3a-4%2Ba-3=highlight%284a-7%29 ALIGN=MIDDLE  ALT=\"a%5B4%5D=a%5B3%5D%2Bd=3a-4%2Ba-3=highlight%284a-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .\r<BR>\n" );
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document.write( "ANOTHER WAY (This works only for sequences with an odd number of terms):<BR>\n" );
document.write( "When three numbers are in an arithmetic sequence,<BR>\n" );
document.write( "the middle term is the average of the first and last terms.<BR>\n" );
document.write( "The same thing happens when in the sequence there are<BR>\n" );
document.write( "5 terms, 7 terms, 9 terms, 11 terms, and so on.<BR>\n" );
document.write( "So, the middle (third) term is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28a%2B2%29%2B%285a-10%29%29%2F2%2B%286a-8%29%2F2=highlight%283a-4%29 ALIGN=MIDDLE  ALT=\"%28%28a%2B2%29%2B%285a-10%29%29%2F2%2B%286a-8%29%2F2=highlight%283a-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The second number, the one between <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2B2 ALIGN=MIDDLE  ALT=\"a%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a-4 ALIGN=MIDDLE  ALT=\"3a-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28a%2B2%29%2B%283a-4%29%29%2F2=%284a-2%29%2F2=highlight%282a-1%29 ALIGN=MIDDLE  ALT=\"%28%28a%2B2%29%2B%283a-4%29%29%2F2=%284a-2%29%2F2=highlight%282a-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The fourth number, the one between <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a-4 ALIGN=MIDDLE  ALT=\"3a-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5a-10 ALIGN=MIDDLE  ALT=\"5a-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283a-4%29%2B%285a-10%29%29%2F2=%288a-14%29%2F2=highlight%284a-7%29 ALIGN=MIDDLE  ALT=\"%28%283a-4%29%2B%285a-10%29%29%2F2=%288a-14%29%2F2=highlight%284a-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );