document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=60460>Question 60460</A>: <I><SPAN STYLE=\"word-break: break-all;\"> mama mia! for some reason, these sequences are just driving me mad! i would appreciate if you could help me with a few more problems. hopefully, something will click in my head after this. <BR>\n" );
document.write( "Instructions: write the general term of the sequence:\r<BR>\n" );
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document.write( "#1.  1,2,3,4,5,6,...\r<BR>\n" );
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document.write( "(answer here) -> Nth term:____<BR>\n" );
document.write( "i'm pretty sure the answer is just plain N, but i'm not sure. \r<BR>\n" );
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document.write( "#2.  1,2,4,8,16,... \r<BR>\n" );
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document.write( "(answer here) -> Nth term: ___<BR>\n" );
document.write( "I know the answer involves the number 2 and N, but i'm not sure how to put them together correctly.\r<BR>\n" );
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document.write( "#10.  1,-1,1,-1,1,-1,...\r<BR>\n" );
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document.write( "Nth term:__<BR>\n" );
document.write( "this one just left me clueless. i think it's -1n^0, but, i'm not sure. \r<BR>\n" );
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document.write( "#9.  -1,4,-9,16,-25,...<BR>\n" );
document.write( "Nth term:__<BR>\n" );
document.write( "again, i think it's -n^3, but i'm not positive. \r<BR>\n" );
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document.write( "I'm also having trouble with adding terms in a sequence. i have a formula: [(first term + last term)(number of terms)]/2. but i'm not sure how i would apply it to sequences involving exponents.\r<BR>\n" );
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document.write( "Instructions: write the sum\r<BR>\n" );
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document.write( "#2. 1+3+9+27+81+...+1*3^101<BR>\n" );
document.write( "Now, am i correct in assuming that 1*3 is the general term of the sequence and that the last term is the 101st value of 1*3?\r<BR>\n" );
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document.write( "#5  2+7+12+17+...+97<BR>\n" );
document.write( "just plain lost on this one. \r<BR>\n" );
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document.write( "again, i thank you for your help in advance<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #41536 by </B><A HREF=/tutors/aboutme.mpl?userid=praseena><B>praseena(37)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=praseena><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=41536\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> first series is 1,2,3,4,5,6,7,..........<BR>\n" );
document.write( "this is arithmatic series<BR>\n" );
document.write( "here the first term is 1 and the common difference is i\r<BR>\n" );
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document.write( "now   N th term of an arithmatic progression is given as  a+(N-1)d,  where a is the first term,N is the  Nth term and d is the common difference.\r<BR>\n" );
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document.write( "so here the Nth term is   1 + ( N - 1 ) * 1 = 1 + N - 1 = <BR>\n" );
document.write( "understood?<BR>\n" );
document.write( "good<BR>\n" );
document.write( "now next problem\r<BR>\n" );
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document.write( "The series is 1,2,4,8,6,........\r<BR>\n" );
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document.write( "this is also an arithmaticseries\r<BR>\n" );
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document.write( "here the first term is 1 and the common difference is 2\r<BR>\n" );
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document.write( "so the Nth term is given as,\r<BR>\n" );
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document.write( "  1 + ( N - 1 ) * 2 = 1 + 2N -2<BR>\n" );
document.write( "           = 2N - 1<BR>\n" );
document.write( "so for this series Nth term is 2N-1.<BR>\n" );
document.write( "understood?\r<BR>\n" );
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document.write( "Next series is  1,-1,1,-1,1,-1,........\r<BR>\n" );
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document.write( " this series is a geometric series and here the first term is 1 and common ratio is -1\r<BR>\n" );
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document.write( "here the N th term is given by the formula, \r<BR>\n" );
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document.write( "An = a * r ^(n-1), where 'a' is the  first term and 'r ' is the common ratio and ' n' represents  nth  term\r<BR>\n" );
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document.write( "so here the nth term is = 1 * ( -1 ) ^ (n-1)<BR>\n" );
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document.write( "here two possibilities are there,<BR>\n" );
document.write( "one is ,  if  n  is an even number then ( n -1) is an odd number.<BR>\n" );
document.write( "which means that (-1) ^( an odd number ) is always -1\r<BR>\n" );
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document.write( "if n is an odd number then (n-1) is an even number,  which means (-1)^(an even number) is always an even number.\r<BR>\n" );
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document.write( "so we can conclude this answer like this,<BR>\n" );
document.write( " if n is an even number, for the given series the nth term is -1<BR>\n" );
document.write( "and if n is an odd number the nth term of the series is +1.\r<BR>\n" );
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document.write( "understood?\r<BR>\n" );
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document.write( "-1,4,-9,16,-25,...<BR>\n" );
document.write( "here terms come like this <BR>\n" );
document.write( "first term is -1,  we can put it as -1*(1)^2\r<BR>\n" );
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document.write( "second term is 4,  ==> - 1*(2)^2\r<BR>\n" );
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document.write( "third term is -9, that is,  -1*(3)^2 \r<BR>\n" );
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document.write( "and so on......<BR>\n" );
document.write( "so we can write the nth term as,    -1(n)^2<BR>\n" );
document.write( "clear?<BR>\n" );
document.write( "o.k.\r<BR>\n" );
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document.write( "next one is g<BR>\n" );
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document.write( " 1+3+9+27+81+...+.........\r<BR>\n" );
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document.write( "first we have to identify the series.\r<BR>\n" );
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document.write( "here  the terms are like this\r<BR>\n" );
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document.write( "first term is  1\r<BR>\n" );
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document.write( "second term is 3, which can be written as 1*3\r<BR>\n" );
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document.write( "third term is 9, ===>  1*3^2\r<BR>\n" );
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document.write( "fourth term is 27=1*3^3\r<BR>\n" );
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document.write( "and so on\r<BR>\n" );
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document.write( "so this is a geometric series.\r<BR>\n" );
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document.write( "the sum of nth term of a series given by the formula,<BR>\n" );
document.write( "(Otherwise we can make out this from the above formation)\r<BR>\n" );
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document.write( "Sn = a * r ^ (n-1)<BR>\n" );
document.write( "   = 1 * 3 ^(n-1)<BR>\n" );
document.write( "   = 1 * 3 ^ (n-1).<BR>\n" );
document.write( "clear?<BR>\n" );
document.write( "o.k.?<BR>\n" );
document.write( "now your doubt is,\r<BR>\n" );
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document.write( "1+3+9+27+81+...+1*3^101\r<BR>\n" );
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document.write( " am i correct in assuming that 1*3 is the general term of the sequence and that the last term is the 101st \r<BR>\n" );
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document.write( "here  1 * 3 ^101 MEANS this is the 100 th term of the series.\r<BR>\n" );
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document.write( "that means 1*3^(n-1) is the general term of the series.\r<BR>\n" );
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document.write( "o.k.?\r<BR>\n" );
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document.write( "next one is,    <BR>\n" );
document.write( "2+7+12+17+...+97\r<BR>\n" );
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document.write( "here the first term is 2\r<BR>\n" );
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document.write( "second term is 7= 2+5\r<BR>\n" );
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document.write( "third term is  12= 7+5\r<BR>\n" );
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document.write( "fourth term is 17=12+5<BR>\n" );
document.write( "and so on......\r<BR>\n" );
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document.write( "thus the series forms by adding  5 to the previous term.\r<BR>\n" );
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document.write( "that is this one is an arithmatic series\r<BR>\n" );
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document.write( "here sum of  first n terms of a series is given by the formulais,<BR>\n" );
document.write( "n/2(first term +last term)\r<BR>\n" );
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document.write( "hwere the first term is  2 and the laqst term is 97so the sum of  the seris is <BR>\n" );
document.write( "n/2(2+97)\r<BR>\n" );
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document.write( "for calculating this sum, we need number of terms. right?\r<BR>\n" );
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document.write( "for that first of find out the number of terms in the series\r<BR>\n" );
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document.write( "we have the formula, a+(n-1)d for the nth term, here take 97 as the nth term\r<BR>\n" );
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document.write( "which comes like this,<BR>\n" );
document.write( "a + ( n - 1 ) d = 97<BR>\n" );
document.write( "2 + ( n -1) * 5 = 97\r<BR>\n" );
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document.write( "now subtract 2 from bopth sides of the equation<BR>\n" );
document.write( "==> (n-1) * 5 = 95\r<BR>\n" );
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document.write( "divide by 5 on both sides\r<BR>\n" );
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document.write( "==> (n-1) = 95 / 5<BR>\n" );
document.write( "==> n -1 = 19\r<BR>\n" );
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document.write( "add 1 on both sides of the equation<BR>\n" );
document.write( "==> n =20\r<BR>\n" );
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document.write( "so the number of terms in the given series  is 20.  right?\r<BR>\n" );
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document.write( "so sum of the 20 terms of the given series is,\r<BR>\n" );
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document.write( "20 /2 (2 + 97 )\r<BR>\n" );
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document.write( "10 * 99 = 990\r<BR>\n" );
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document.write( "so the answer is 990.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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