document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=39508>Question 39508</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I really need some help!!  (Fast!!!!) Please....<BR>\n" );
document.write( "Using the index of a series as the domain an dthe value of the series as the range, is the series a function?<BR>\n" );
document.write( "Include in ans: <BR>\n" );
document.write( "Which one of the basic functions(linear, quadratic, rational, or exponential) is related to the arithmetic series?<BR>\n" );
document.write( "Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the geometric series?<BR>\n" );
document.write( "Give real life examples of both arithmetic and geometric sequences and series. Explain how these might affect you personally?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2. 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( "Ans:<BR>\n" );
document.write( "Show work below:\r<BR>\n" );
document.write( "\n" );
document.write( "b) Using the formula for the nth term of an arithmetic sequence, what is 101st term? Ans:\r<BR>\n" );
document.write( "\n" );
document.write( "c) Using the formula for the sum of an aritmetic series, what is the sum of the first 20 terms?<BR>\n" );
document.write( "Ans:\r<BR>\n" );
document.write( "\n" );
document.write( "d) Using the formula for the sum of an aritmetic series, what is the sum of the first 30 terms?<BR>\n" );
document.write( "Ans:\r<BR>\n" );
document.write( "\n" );
document.write( "e)What observation can you make about these sums of this series (HINT: It would be beneficial to find a few more sums like the sum of the first 2, then the first 3, etc..)? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #24945 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=24945\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Using the index of a series as the domain an dthe value of the series as the range, is the series a function?<BR>\n" );
document.write( "Include in ans:<BR>\n" );
document.write( "Which one of the basic functions(linear, quadratic, rational, or exponential) is related to the arithmetic series?TN=A+(N-1)*D.............LINEAR EQN.<BR>\n" );
document.write( "Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the geometric series?TN=A*R^(N-1)............EXPONENTIAL <BR>\n" );
document.write( "Give real life examples of both arithmetic and geometric sequences and series. Explain how these might affect you personally? <BR>\n" );
document.write( "REAL LIFE EXAMPLES...<BR>\n" );
document.write( "ARITHMATIC / PROGRESSION/SERIES....A.P.<BR>\n" );
document.write( "SUPPOSE YOU ARE SAVING YOUR MONEY IN A BANK BY<BR>\n" );
document.write( "SYSTEMATIC PLAN OF<BR>\n" );
document.write( "DEPOSITING 100 $ A MONTH...THEN STARTING WITH A 100$<BR>\n" );
document.write( "ACCOUNT YOUR<BR>\n" );
document.write( "MONEY IN CREDIT WITHOUT INTEREST ,WOULD BE AN EXAMPLE<BR>\n" );
document.write( "OF A.P...IT<BR>\n" );
document.write( "WILL BE..... TAKING MONTH AS AN INDEX...<BR>\n" );
document.write( "100,200,300,400......<BR>\n" );
document.write( "GEOMETRIC PROGRESSION/SERIES.....G.P.<BR>\n" );
document.write( "IN A SIMILAR WAY SUPPOSE YOU DEPOSITED 1000 $ IN A<BR>\n" );
document.write( "BANK FOR INTEREST<BR>\n" );
document.write( "OF 4% PER YEAR,AND THE INTEREST IS CALCULATED AT THE<BR>\n" );
document.write( "END EVERY YEAR<BR>\n" );
document.write( "AND ADDED TO THE PRINCIPAL,THEN THE AMOUNT GROWN AT<BR>\n" );
document.write( "THE END OF YEAR IS<BR>\n" );
document.write( "AN EXAMPLE OF G.P.TAKING YEAR AS N INDEX....THE AMOUNT<BR>\n" );
document.write( "AT THE END OF<BR>\n" );
document.write( "SUCCESSIVE YEARS IS .....<BR>\n" );
document.write( "1000,1000*1.04,1000*1.04^2,1000*1.04^3....ETC...<BR>\n" );
document.write( "KNOWING THAT A G.P WILL YIELD MORE THAN A.P. ,WE BETTER PUT OUR MONEY IN INTERESTING EARNING SECURITY THAN AT HOME WHERE NO INTEREST ACCRUES.<BR>\n" );
document.write( "------------------------------------------------------------------------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "SEE THE FOLLOWING EXAMPLE WHICH IS PRACTICALLY SAME<BR>\n" );
document.write( "---------------------------------------------------<BR>\n" );
document.write( "1)Use the arithmetic<BR>\n" );
document.write( "sequence of numbers 2, 4, 6, 8, 10&#65533; to find the<BR>\n" );
document.write( "following:<BR>\n" );
document.write( "a)What is d, the difference between any 2 terms?<BR>\n" );
document.write( "Answer:<BR>\n" );
document.write( "Show work in this space.\r<BR>\n" );
document.write( "\n" );
document.write( "b)Using the formula for the nth term of an arithmetic<BR>\n" );
document.write( "sequence, what is 101st term? Answer:<BR>\n" );
document.write( "Show work in this space.\r<BR>\n" );
document.write( "\n" );
document.write( "c)Using the formula for the sum of an arithmetic<BR>\n" );
document.write( "series, what is the sum of the first 20 terms?<BR>\n" );
document.write( "Answer:<BR>\n" );
document.write( "Show work in this space.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "d)Using the formula for the sum of an arithmetic<BR>\n" );
document.write( "series, what is the sum of the first 30 terms?<BR>\n" );
document.write( "Answer:<BR>\n" );
document.write( "Show work in this space.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "e)What observation can you make about these sums of<BR>\n" );
document.write( "this series (HINT: It would be beneficial to find a<BR>\n" );
document.write( "few more sums like the sum of the first 2, then the<BR>\n" );
document.write( "first 3, etc.)?<BR>\n" );
document.write( "Answer:<BR>\n" );
document.write( "1 solutions<BR>\n" );
document.write( "--------------------------------------------------------------------------------<BR>\n" );
document.write( "Answer 16520 by venugopalramana(1619) on 2006-03-10<BR>\n" );
document.write( "07:41:16 (Show Source):<BR>\n" );
document.write( "1)Use the arithmetic sequence of numbers 2, 4, 6, 8,<BR>\n" );
document.write( "10&#65533; 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" );
document.write( "Show work in this space.<BR>\n" );
document.write( "D= COMMON DIFFERENCE BETWEEN 2 CONSECUTIVE TERMS<BR>\n" );
document.write( "4-2=6-4=8-6=10-8=2....CONSTANT...THIS IS THE PROPERTY<BR>\n" );
document.write( "OF ARITHMATIC PROGRESSION<BR>\n" );
document.write( "b)Using the formula for the nth term of an arithmetic<BR>\n" );
document.write( "sequence, what is 101st term? Answer:<BR>\n" );
document.write( "Show work in this space.<BR>\n" );
document.write( "TN=A+(N-1)D=2+(N-1)2=2N<BR>\n" );
document.write( "T101=2*101=202<BR>\n" );
document.write( "c)Using the formula for the sum of an arithmetic<BR>\n" );
document.write( "series, what is the sum of the first 20 terms?<BR>\n" );
document.write( "Answer:<BR>\n" );
document.write( "Show work in this space.<BR>\n" );
document.write( "SN=(N/2){2A+(N-1)D}=(N/2){2*2+(N-1)2}=(N/2)(2N+2)=N^2+N<BR>\n" );
document.write( "S20=20^2+20=420<BR>\n" );
document.write( "d)Using the formula for the sum of an arithmetic<BR>\n" );
document.write( "series, what is the sum of the first 30 terms?<BR>\n" );
document.write( "Answer:<BR>\n" );
document.write( "Show work in this space.<BR>\n" );
document.write( "S30=30^2+30=930<BR>\n" );
document.write( "e)What observation can you make about these sums of<BR>\n" );
document.write( "this series (HINT: It would be beneficial to find a<BR>\n" );
document.write( "few more sums like the sum of the first 2, then the<BR>\n" );
document.write( "first 3, etc.)?<BR>\n" );
document.write( "Answer: 1.THE SUM IS A QUDRATATIC IN N.<BR>\n" );
document.write( "2.IT IS EQUAL TO THE SUM OF NUMBER OF TERMS AND ITS<BR>\n" );
document.write( "SQUARE  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );