document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=983047>Question 983047</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ann goes swimming regularly. She wants to improve her fitness, so she decides to swim 10 lengths in the first session and increase the number of lengths she swims by 2 every session. When she reaches 50 lengths in a session, she will not increase the number any further. After how many sessions does Ann swim 50 lengths for the first time? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #603933 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><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=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=603933\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is an example of an arithmetic series with first term 10 and common difference 2. We also have that some nth term is 50.\r<BR>\n" );
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document.write( "We can relate the nth term with the 1st term by the following formula:\r<BR>\n" );
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document.write( "a_n = a_1 + d(n-1)\r<BR>\n" );
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document.write( "Here, a_n = 50,  a_1 = 10 and d = 2. This is enough to solve.\r<BR>\n" );
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document.write( "50 = 10 + 2(n-1)\r<BR>\n" );
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document.write( "40 = 2(n-1)\r<BR>\n" );
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document.write( "20 = n-1\r<BR>\n" );
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document.write( "21 = n\r<BR>\n" );
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document.write( "ANSWER -> So on the 21st session, Anne swims 50 lengths. To see it the long way:\r<BR>\n" );
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document.write( "I'll label session # on the left and number of lengths on the right.\r<BR>\n" );
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document.write( " 1 | 10<BR>\n" );
document.write( " 2 | 12<BR>\n" );
document.write( " 3 | 14<BR>\n" );
document.write( " 4 | 16<BR>\n" );
document.write( " 5 | 18<BR>\n" );
document.write( " 6 | 20<BR>\n" );
document.write( " 7 | 22<BR>\n" );
document.write( " 8 | 24<BR>\n" );
document.write( " 9 | 26<BR>\n" );
document.write( "10 | 28<BR>\n" );
document.write( "11 | 30<BR>\n" );
document.write( "12 | 32<BR>\n" );
document.write( "13 | 34<BR>\n" );
document.write( "14 | 36<BR>\n" );
document.write( "15 | 38<BR>\n" );
document.write( "16 | 40<BR>\n" );
document.write( "17 | 42<BR>\n" );
document.write( "18 | 44<BR>\n" );
document.write( "19 | 46<BR>\n" );
document.write( "20 | 48<BR>\n" );
document.write( "21 | 50<BR>\n" );
document.write( "22 | 50<BR>\n" );
document.write( "23 | 50<BR>\n" );
document.write( "... </SPAN>\n" );
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