document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1165566>Question 1165566</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Generate the geometric sequence. Give the first 5 terms<BR>\n" );
document.write( "A) First term is 7 and common ratio is 4 <BR>\n" );
document.write( "I got the answer 7,28,112,448,1792<BR>\n" );
document.write( "B)First term is 10 and common ratio is -3<BR>\n" );
document.write( "I got the answer 10,-30,90,-270,810<BR>\n" );
document.write( "C)First term is 25 and third term is 900<BR>\n" );
document.write( "I got the answer 25,150,900,5400,32400<BR>\n" );
document.write( "D)First term is 8 and the fourth term is 1000<BR>\n" );
document.write( "I got the answer 8,40,200,1000,5000<BR>\n" );
document.write( "E)First term is -5 and the fifth term is -6480<BR>\n" );
document.write( "I got the answer-5,-30,-180,-1080,-6480<BR>\n" );
document.write( "I’m not quite sure about my answers 😅 did I do something wrong?\r<BR>\n" );
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document.write( "May I ask for your assistance in this two below I don’t quite get on how to get it’s terms because I’m not good at fractions <BR>\n" );
document.write( "F)Fifth term is 3/256 and common ratio is 2<BR>\n" );
document.write( "G)Sixth term is 7/4 and the seventh term is 1/2\r<BR>\n" );
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document.write( "Thank you for your assistance in advance 😁 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #790078 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=790078\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formula for a geometric series is An = A1 * r ^ (n-1)<BR>\n" );
document.write( "each succeeding term is multiplied by r<BR>\n" );
document.write( "each preceding term is divided by 4.\r<BR>\n" );
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document.write( "A is correct.\r<BR>\n" );
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document.write( "B is correct.\r<BR>\n" );
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document.write( "C is correct.\r<BR>\n" );
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document.write( "D is correct.\r<BR>\n" );
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document.write( "E is correct.\r<BR>\n" );
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document.write( "so far you're did well.\r<BR>\n" );
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document.write( "F says the fifth term is 3/256 and the common ratio is 2.\r<BR>\n" );
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document.write( "the formula is An = A1 * r ^ (n-1)<BR>\n" );
document.write( "replace A5 with 3/256 and r with 2 and n with 5 and the formula says 3/256 = A1 * 2 ^ 4 which becomes 3/256 = A1 * 16.<BR>\n" );
document.write( "solve for A1 to get:<BR>\n" );
document.write( "A1 = 3/256 / 16 which is the same as 3/256 * 1/16 which is equal to 3/4096.\r<BR>\n" );
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document.write( "A1 would be 3/4096.<BR>\n" );
document.write( "A2 would be 2 * that = 6/4096.<BR>\n" );
document.write( "A3 would be 2 * that = 12/4096.<BR>\n" );
document.write( "A4 would be 2 * that = 24/4096.<BR>\n" );
document.write( "A5 would be 2 * that = 48/4096.\r<BR>\n" );
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document.write( "that is your answer.<BR>\n" );
document.write( "the only thing left to do, if they require it, is to simplify the fraction.<BR>\n" );
document.write( "note that, for practical purposes, you do not have to simplify it since your calculator can easily handle these numbers.\r<BR>\n" );
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document.write( "in the first term, the denominator and the numerator are not divisible by any common integer, so it remains at 3/4096.\r<BR>\n" );
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document.write( "in  the second term, the denominator and the numerator are divisible by 2.<BR>\n" );
document.write( "divide both numerator and denominator by 2 and you get 3/2048.\r<BR>\n" );
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document.write( "in the third term, the denominator and the numerator are divisible by 4.<BR>\n" );
document.write( "divide both numerator and denominator by 4 and you get 3/1024\r<BR>\n" );
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document.write( "in the fourth term, the denominator and the numerator are divisible by 8.<BR>\n" );
document.write( "divide both numerator and denominator by 8 and you get 3/512.\r<BR>\n" );
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document.write( "in the fifth term, the denominator and the numerator are divisible by 16.<BR>\n" );
document.write( "divide both numerator and denominator by 16 and you get 3/256.\r<BR>\n" );
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document.write( "your sequence, which was 3/1096, 6/4096, 12/4096, 24/4096, 48/4096, becomes:<BR>\n" );
document.write( "3/4096, 3/2048, 3/1024, 3/512, 3/256.\r<BR>\n" );
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document.write( "G says the sixth term is 7/4 and the seventh term is 1/2.\r<BR>\n" );
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document.write( "the succeeding term is equal to r times the preceding term.<BR>\n" );
document.write( "this means that 7/4 * r = 1/2.<BR>\n" );
document.write( "multiply both sides of this equation by 4/7 to get:<BR>\n" );
document.write( "r = 1/2 * 4/7 = 4/14 = 2/7.<BR>\n" );
document.write( "the common ratio is 2/7.\r<BR>\n" );
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document.write( "to confirm, multiply 7/4 by 2/7 to get 14/28 = 1/2.<BR>\n" );
document.write( "the common ratio of 2/7 is correct.\r<BR>\n" );
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document.write( "at this point in time, you shouldn't have to simplify fractions manually, especially monsters like the ones this problem gives you.\r<BR>\n" );
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document.write( "there are some calculators that can do that for you.<BR>\n" );
document.write( "they can convert answers in decimal form to answers in simplified fraction form.\r<BR>\n" );
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document.write( "my calculator is the TI-84 Plus, which does both of these for me.\r<BR>\n" );
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document.write( "for example, i put 3764768 / 2151296 in the calculator and it tells me that the answer is 1.75 in decimal form.<BR>\n" );
document.write( "to convert that answer to simplified fraction form, i do the following.<BR>\n" );
document.write( "the answer in decimal form is in the calculator<BR>\n" );
document.write( "i leave it there as is.<BR>\n" );
document.write( "i press the MATH button.<BR>\n" );
document.write( "i select 1:0>Frac<BR>\n" );
document.write( "the calculator tells me the fraction is 7/4.\r<BR>\n" );
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document.write( "the number that i gave it was the fraction 3764768/2151296<BR>\n" );
document.write( "the calculator gave me the answer in decimal form.<BR>\n" );
document.write( "i then have the calculator convert that to simplified fraction form equal to 7/4.<BR>\n" );
document.write( "this was the 6th term in the sequence.<BR>\n" );
document.write( "the calculator told me that the sixth term is equal to 7/4 in simplified fraction form.\r<BR>\n" );
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document.write( "this confirmed for me that the ratio of 2/7 was correct.\r<BR>\n" );
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document.write( "if you got yourself a TI-84 Plus, you can do the same thing too.<BR>\n" );
document.write( "they're about 100 dollars new, plus or minus, but you can get a used one on ebay for about 40, plus or minus.\r<BR>\n" );
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document.write( "in the absence of that, you can use an online fraction simplifier.\r<BR>\n" );
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document.write( "the one that i found is at <a  rel=nofollow HREF= \"http://www.alcula.com/calculators/math/simplify-fractions/\" target = \"_blank\">http://www.alcula.com/calculators/math/simplify-fractions/</a>\r<BR>\n" );
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document.write( "it seems to work quite well.\r<BR>\n" );
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document.write( "you give it the numerator and the denominator and it tells you the fraction in simplified form.\r<BR>\n" );
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document.write( "for example, i told it the numerator was 3764768 and the denominator was 2151296 and it told me that the simplified fraction was 7/4.\r<BR>\n" );
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document.write( "with a tool like this, you can keep your answer in unsimplified form and then have this tool simplify it for you.\r<BR>\n" );
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document.write( "you still need to know how to do fraction arithmetic, but the burden of simplifying the answer has been removed.\r<BR>\n" );
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document.write( "since you probably don't have the TI-84 Plus, i'll use the online calculator to simplify the fractions for you.\r<BR>\n" );
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document.write( "we determined above, that the common ratio is 2/7.\r<BR>\n" );
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document.write( "to find the preceding term, we have to divide by (2/7).<BR>\n" );
document.write( "this is the same thing as multiplying by 7/2.<BR>\n" );
document.write( "so, to find the preceding term, we have to multiply the current term by 7/2.\r<BR>\n" );
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document.write( "the common ratio is 2/7.<BR>\n" );
document.write( "to find the next term, we multiply by 2/7.<BR>\n" );
document.write( "to find the preceding term, we multiply by 7/2.\r<BR>\n" );
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document.write( "we'll work our way down to the first term.\r<BR>\n" );
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document.write( "sixth term is 7/4<BR>\n" );
document.write( "fifth term is 7/4 * 7/2 = 49/8<BR>\n" );
document.write( "fourth term is 49/8 * 7/2 = 343/16<BR>\n" );
document.write( "third term is 343/16 * 7/2 = 2401/32<BR>\n" );
document.write( "second term is 2401/32 = 16807/64<BR>\n" );
document.write( "first term is 117649/128\r<BR>\n" );
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document.write( "the sequence, in unsimplified form, appears to be:\r<BR>\n" );
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document.write( "first term is 117649/128<BR>\n" );
document.write( "second term is 16807/64<BR>\n" );
document.write( "third term is 2401/32<BR>\n" );
document.write( "fourth term is 343/16<BR>\n" );
document.write( "fifth term is 49/8<BR>\n" );
document.write( "sixth term is 7/4\r<BR>\n" );
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document.write( "i put these fractions into the fraction simplifier and it told me that they are all already in simplified form.\r<BR>\n" );
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document.write( "since none of these fractions can be simplified any further than they already are, then that's the answer.\r<BR>\n" );
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document.write( "with the online fraction simplifier, for example, i would enter 117649 as the numerator and 128 as the denominator and the calculator would tell me that the simplified fraction was 117649/128 which means that it was already in simplified form.\r<BR>\n" );
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document.write( "if i wanted to use the geometric sequence formula, i would have done the following.<BR>\n" );
document.write( "i would have solved for r as i did before to get r = 2/7<BR>\n" );
document.write( "the general formula is An = A1 * r ^ (n-1)<BR>\n" );
document.write( "when n = 6, given the  numbers that i have, the formula becomes:<BR>\n" );
document.write( "7/4 = A1 * (2/7) ^ 5<BR>\n" );
document.write( "(2/7) ^ 5 becomes 2^5 / 7^5 = 32/16807.<BR>\n" );
document.write( "the formula becomes:<BR>\n" );
document.write( "7/4 = A1 * 32/16807.<BR>\n" );
document.write( "multiply both sides of this formula by 16807/32 to get:<BR>\n" );
document.write( "7/4 * 16807/32 = A1<BR>\n" );
document.write( "solve for A1 to get A1 = (7 * 16807) / (4 * 32) = 117649/128.\r<BR>\n" );
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document.write( "that's my first term.<BR>\n" );
document.write( "each succeeding term will be multiplied by 2/7 until i get to the 6th term.<BR>\n" );
document.write( "i take the sequence to the 6th term because that term is what i use to confirm my answer is correct.\r<BR>\n" );
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document.write( "without simplifying the fractions, i get:<BR>\n" );
document.write( "first  term = 117649/128<BR>\n" );
document.write( "second term = 235298/896<BR>\n" );
document.write( "third term = 470596/6272<BR>\n" );
document.write( "four term = 941192/43904<BR>\n" );
document.write( "fifth term = 1882384/307328<BR>\n" );
document.write( "sixth term = 3764768/2151296\r<BR>\n" );
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document.write( "i use  the fraction simplifier to determine that the sixth term is 7/4.<BR>\n" );
document.write( "since this is what it's supposed to be, then the sequence is correct.\r<BR>\n" );
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document.write( "i then simplify all the fractions from the first term to the fifth term.<BR>\n" );
document.write( "i get:\r<BR>\n" );
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document.write( "first  term = 117649/128 = 117649/128<BR>\n" );
document.write( "second term = 235298/896 = 16807/64<BR>\n" );
document.write( "third term = 470596/6272 = 2401/32<BR>\n" );
document.write( "four term = 941192/43904 = 343/16<BR>\n" );
document.write( "fifth term = 1882384/307328 = 49/8<BR>\n" );
document.write( "sixth term = 3764768/2151296 = 7/4\r<BR>\n" );
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document.write( "i previously got, by working backwards from the sixth term, the following sequence:\r<BR>\n" );
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document.write( "first term is 117649/128<BR>\n" );
document.write( "second term is 16807/64<BR>\n" );
document.write( "third term is 2401/32<BR>\n" );
document.write( "fourth term is 343/16<BR>\n" );
document.write( "fifth term is 49/8<BR>\n" );
document.write( "sixth term is 7/4\r<BR>\n" );
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document.write( "the answer i got by using the formula is the same as the answer i got by working backward from the sixth term.\r<BR>\n" );
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document.write( "in this case, working backward from the sixth term was easier.\r<BR>\n" );
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document.write( "use of the ti-84 plus is much easier to convert your answer to simplified fraction form, but the fraction simplifier is also not very difficult to use.\r<BR>\n" );
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document.write( "again:<BR>\n" );
document.write( "calculator i used is TI-84 Plus<BR>\n" );
document.write( "online fraction simplifier i used is at <a  rel=nofollow HREF= \"http://www.alcula.com/calculators/math/simplify-fractions/\" target = \"_blank\">http://www.alcula.com/calculators/math/simplify-fractions/</a>\r<BR>\n" );
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document.write( "if you want more information on fraction arithmetic, here's a reference.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.mathsisfun.com/algebra/fractions-algebra.html\" target = \"_blank\">https://www.mathsisfun.com/algebra/fractions-algebra.html</a>.\r<BR>\n" );
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document.write( "if you want to simplify fractions manually, here's a reference.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.mathsisfun.com/simplifying-fractions.html\" target = \"_blank\">https://www.mathsisfun.com/simplifying-fractions.html</a>\r<BR>\n" );
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document.write( "this reference also has a fraction simplifier that will simplify the fraction for you. </SPAN>\n" );
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