document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=551085>Question 551085</A>: <I><SPAN STYLE=\"word-break: break-all;\"> for part (a) find the sum of the first n terms of the arithmetic series. for part (b) find n for the given sum Sn.\r<BR>\n" );
document.write( "\n" );
document.write( "45. 3+8+13+18+23+...<BR>\n" );
document.write( "a. n=20<BR>\n" );
document.write( "b. Sn=366\r<BR>\n" );
document.write( "\n" );
document.write( "46. 50+42+34+26+18+...<BR>\n" );
document.write( "a. n=40<BR>\n" );
document.write( "b. Sn=182\r<BR>\n" );
document.write( "\n" );
document.write( "47. -10+(-5)+0+5+10+...<BR>\n" );
document.write( "a. n=19<BR>\n" );
document.write( "b. Sn=375\r<BR>\n" );
document.write( "\n" );
document.write( "48. 34+31+28+25+22+...<BR>\n" );
document.write( "a. n=32<BR>\n" );
document.write( "b. Sn=-12\r<BR>\n" );
document.write( "\n" );
document.write( "49. 2+9+16+23+30+...<BR>\n" );
document.write( "a. n=68<BR>\n" );
document.write( "b. Sn=1661\r<BR>\n" );
document.write( "\n" );
document.write( "50. 2+16+30+44+58+...<BR>\n" );
document.write( "a. n=24<BR>\n" );
document.write( "b. Sn=2178\r<BR>\n" );
document.write( "\n" );
document.write( "please show your work also so i know how to do it,<BR>\n" );
document.write( "thank you for ur help and happy new year! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #359420 by </B><A HREF=/tutors/aboutme.mpl?userid=mathstutor458><B>mathstutor458(57)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathstutor458><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=359420\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 45. 3+8+13+18+23+... is arithmatic sequence<BR>\n" );
document.write( "first term a1= 3, difference d=8-3=5\r<BR>\n" );
document.write( "\n" );
document.write( "a. n=20<BR>\n" );
document.write( "The sum of the first n terms of the arithmetic series Sn=(n/2)(2a1+(n-1)d)<BR>\n" );
document.write( "the sum of the first 20 terms of the arithmetic series=(20/2)(2*3 + (20-1)*5)<BR>\n" );
document.write( "=10*(6+19*5)=10*(6+95)<BR>\n" );
document.write( "=10*101=1010  ----->answer\r<BR>\n" );
document.write( "\n" );
document.write( "b. Sn=366 <BR>\n" );
document.write( "The sum of the first n terms of the arithmetic series Sn=(n/2)(2a1+(n-1)d)<BR>\n" );
document.write( "(n/2)(2a1+(n-1)d)=366<BR>\n" );
document.write( "n(2*3+(n-1)5)=366*2<BR>\n" );
document.write( "6n+5n^2-5n=732<BR>\n" );
document.write( "5n^2+n-732=0<BR>\n" );
document.write( "5n^2-60n+61n-732=0<BR>\n" );
document.write( "5n(n-12)+61(n-12)=0<BR>\n" );
document.write( "(5n+61)(n-12)=0<BR>\n" );
document.write( "Therefore, n=12 positive number,we dont consider fractional numbers.<BR>\n" );
document.write( "n=12--------> answer\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "46. 50+42+34+26+18+...is arithmatic sequence<BR>\n" );
document.write( "first term a1= 50, difference d=42-50=-8<BR>\n" );
document.write( "a. n=40<BR>\n" );
document.write( "The sum of the first n terms of the arithmetic series Sn=(n/2)(2a1+(n-1)d)<BR>\n" );
document.write( "the sum of the first 40 terms of the arithmetic series=(40/2)(2*50 + (40-1)(-8))<BR>\n" );
document.write( "=20*(100+39(-8))<BR>\n" );
document.write( "=20*(100-312)<BR>\n" );
document.write( "=20*(-212)=-4240  -------> is sum of 40 numbers(answer)\r<BR>\n" );
document.write( "\n" );
document.write( "b. Sn=182 <BR>\n" );
document.write( "The sum of the first n terms of the arithmetic series Sn=(n/2)(2a1+(n-1)d)<BR>\n" );
document.write( "(n/2)(2a1+(n-1)d)=182<BR>\n" );
document.write( "n(2*50+(n-1)(-8))=182*2<BR>\n" );
document.write( "n(100-8n+8)=364<BR>\n" );
document.write( "-8n^2+108n-364=0<BR>\n" );
document.write( "-8n^2+56n+52n-364=0<BR>\n" );
document.write( "-8n(n-7)+52(n-7)=0<BR>\n" );
document.write( "(n-7)(-8n+52)=0<BR>\n" );
document.write( "n=7 positive number,we dont consider fractional numbers.<BR>\n" );
document.write( "n=7--------> answer\r<BR>\n" );
document.write( "\n" );
document.write( "47. -10+(-5)+0+5+10+...is arithmatic sequence<BR>\n" );
document.write( "first term a1= -10, difference d=-5-(-10)=-5+10=5<BR>\n" );
document.write( "a. n=19<BR>\n" );
document.write( "The sum of the first n terms of the arithmetic series Sn=(n/2)(2a1+(n-1)d)<BR>\n" );
document.write( "the sum of the first 19 terms of the arithmetic series=(19/2)(2*(-10)+(19-1)5)<BR>\n" );
document.write( "=(19/2)(-20+18*5)=(19/2)(-20+80)<BR>\n" );
document.write( "=(19/2)60=19*30=570-------> is sum of 19 numbers(answer)\r<BR>\n" );
document.write( "\n" );
document.write( "b. Sn=375<BR>\n" );
document.write( "The sum of the first n terms of the arithmetic series Sn=(n/2)(2a1+(n-1)d)<BR>\n" );
document.write( "(n/2)(2a1+(n-1)d)=375<BR>\n" );
document.write( "(n/2)(2*(-10) + (n-1)(5)) = 375<BR>\n" );
document.write( "(n)(-20+5n-5)=375*2<BR>\n" );
document.write( "5n^2-25n=750<BR>\n" );
document.write( "5n^2-25n-750=0<BR>\n" );
document.write( "5n^2-75n+50n-750=0<BR>\n" );
document.write( "5n(n-15)+50(n-15)=0<BR>\n" );
document.write( "(n-15)(5n+50)=0<BR>\n" );
document.write( "n=15 positive number,we dont consider fractional numbers.<BR>\n" );
document.write( "n=15--------> answer\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "48. 34+31+28+25+22+...is arithmatic sequence<BR>\n" );
document.write( "first term a1= 34, difference d=31-(34)=-3<BR>\n" );
document.write( "a. n=32<BR>\n" );
document.write( "Sn=(n/2)(2a1+(n-1)d)<BR>\n" );
document.write( "S32=(32/2)(2*34+(32-1)(-3))=16*(68-93)=-400\r<BR>\n" );
document.write( "\n" );
document.write( "b. Sn=-12 <BR>\n" );
document.write( "Sn=(n/2)(2a1+(n-1)d)<BR>\n" );
document.write( "(n)(2*34+(n-1)(-3))=-12*2<BR>\n" );
document.write( "68n-3n^2+3n+24=0<BR>\n" );
document.write( "-3n^2+71n+24=0<BR>\n" );
document.write( "(n-24)(-3n-1)=0<BR>\n" );
document.write( "n=24  positive number,we dont consider fractional numbers.<BR>\n" );
document.write( "n=24--------> answer\r<BR>\n" );
document.write( "\n" );
document.write( "49. 2+9+16+23+30+...<BR>\n" );
document.write( "first term a1= 2, difference d=9-2=7<BR>\n" );
document.write( "a. n=68<BR>\n" );
document.write( "Sn=(n/2)(2a1+(n-1)d)<BR>\n" );
document.write( "S68=(68/2)(2*2+(68-1)7)<BR>\n" );
document.write( "=34*(4+469)=16082\r<BR>\n" );
document.write( "\n" );
document.write( "b. Sn=1661 <BR>\n" );
document.write( "Sn=(n/2)(2a1+(n-1)d)<BR>\n" );
document.write( "(n)(2*2+(n-1)7)=1661*2<BR>\n" );
document.write( "4n+7n^2-7n-3322=0<BR>\n" );
document.write( "7n^2-3n-3322=0<BR>\n" );
document.write( "(n-22)(7n+151)=0\r<BR>\n" );
document.write( "\n" );
document.write( "n=22 positive number,we dont consider fractional numbers.<BR>\n" );
document.write( "n=22--------> answer\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "50. 2+16+30+44+58+...<BR>\n" );
document.write( "first term a1= 2, difference d=16-2=14<BR>\n" );
document.write( "a. n=24<BR>\n" );
document.write( "Sn=(n/2)(2a1+(n-1)d)<BR>\n" );
document.write( "S24=(24/2)(2*2+(24-1)14)<BR>\n" );
document.write( "=12(4+322)=12*326=3912\r<BR>\n" );
document.write( "\n" );
document.write( "b. Sn=2178 <BR>\n" );
document.write( "Sn=(n/2)(2a1+(n-1)d)<BR>\n" );
document.write( "(n)(2*2+(n-1)14)=2178*2<BR>\n" );
document.write( "4n+14n^2-14n-4356=0<BR>\n" );
document.write( "14n^2-10n-4356=0<BR>\n" );
document.write( "(n-18)(14n+242)=0<BR>\n" );
document.write( "n=18 positive number,we dont consider fractional numbers.<BR>\n" );
document.write( "n=18--------> answer </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );