document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=494677>Question 494677</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could you help me solve those problems!!!<BR>\n" );
document.write( "1. When the same constant is added to the numbers 60, 100, and 150, a three-term geometric sequence arises. What is the constant ratio of the resulting sequence?<BR>\n" );
document.write( "2. Find all positive integers a and n such that n is greater or equal to 2 and<BR>\n" );
document.write( "a + (a + 1) + (a + 2) + . . . + (a + n - 1) = 100<BR>\n" );
document.write( "Thank you for your help!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #335748 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=335748\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. When the same constant is added to the numbers 60, 100, and 150, a three-term geometric sequence arises. What is the constant ratio of the resulting sequence?<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "Let the constant ratio be \"r\":<BR>\n" );
document.write( "(100+x)/(60+x) = r<BR>\n" );
document.write( "(150+x)/(100+x) = r<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Substitute:<BR>\n" );
document.write( "(100+x)/(60+x) = (150+x)/(100+x) <BR>\n" );
document.write( "---------<BR>\n" );
document.write( "(100+x)^2 = (60+x)(150+x)<BR>\n" );
document.write( "----<BR>\n" );
document.write( "100^2 + 200x + x^2 = 9000 + 210x + x^2<BR>\n" );
document.write( "1000 -10x = 0<BR>\n" );
document.write( "x = 100<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve for \"r\":<BR>\n" );
document.write( "(100+x)/(60+x) = r<BR>\n" );
document.write( "---<BR>\n" );
document.write( "200/160 = r<BR>\n" );
document.write( "r = 5/4<BR>\n" );
document.write( "==========================================\r<BR>\n" );
document.write( "\n" );
document.write( "2. Find all positive integers a and n such that n is greater or equal to 2 and<BR>\n" );
document.write( "a + (a + 1) + (a + 2) + . . . + (a + n - 1) = 100<BR>\n" );
document.write( "---<BR>\n" );
document.write( "There are n terms<BR>\n" );
document.write( "Sum = na + (0+1+2+3+...+n-1) = 100 <BR>\n" );
document.write( "I'll leave the rest to you<BR>\n" );
document.write( "================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "================= </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );