document.write( "Question 48832: 1. Use the geometric sequence of numbers 1, 1/3, 1/9, 1/27... to find the following:
\n" ); document.write( "a. What is r, the ratio between 2 consecutive terms? (show work)
\n" ); document.write( "b. Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms? Carry all calculations to 7 significant figures. (show work)
\n" ); document.write( "c. Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 12 terms? Carry all calculations to 7 significant figures. (show work)
\n" ); document.write( "d. What observation can make about the successive partial sum of this series? In particular, what number does it appear that the sum will always be smaller than? \n" ); document.write( "
Algebra.Com's Answer #32340 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
1. Use the geometric sequence of numbers 1, 1/3, 1/9,\r\n" );
document.write( "1/27... \r\n" );
document.write( "   to find the following:\r\n" );
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document.write( "a. What is r, the ratio between 2 consecutive terms? (show work)\r\n" );
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document.write( "2nd term ÷ 1st term = (1/3)÷1 = 1/3\r\n" );
document.write( "3rd term ÷ 2nd term = (1/9)÷(1/3) = (1/9)×(3/1) = 3/9 = 1/3\r\n" );
document.write( "4th term ÷ 3rd term = (1/27)÷(1/9) = (1/27)×(9/1) = 9/27 = 1/3\r\n" );
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document.write( "So the common ratio, r, must be 1/3\r\n" );
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document.write( "b. Using the formula for the sum of the first n terms of a \r\n" );
document.write( "   geometric series, \r\n" );
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document.write( "      a1(1 - rn)\r\n" );
document.write( "Sn = ------------\r\n" );
document.write( "        1 - r\r\n" );
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document.write( "Where a1 is the first term, r the common ratio, and\r\n" );
document.write( "n is the number of terms.\r\n" );
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document.write( "what is the sum of the first 10 terms?\r\n" );
document.write( "Carry all calculations to 7 significant figures.\r\n" );
document.write( "(show work)\r\n" );
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document.write( "       (1)[1 - (1/3)10]\r\n" );
document.write( "S10 = ------------------\r\n" );
document.write( "           1 - 1/3\r\n" );
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document.write( "       1 - 1/310\r\n" );
document.write( "S10 = ----------- \r\n" );
document.write( "          2/3    \r\n" );
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document.write( "Punching that out on my TI-84\r\n" );
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document.write( "(1-1/3^10)/(2/3) ENTER\r\n" );
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document.write( "get .6666553766\r\n" );
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document.write( "or to 7 figures, .6666554\r\n" );
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document.write( "c. Using the formula for the sum of the first n terms of a\r\n" );
document.write( "geometric series, what is the sum of the first 12 terms?\r\n" );
document.write( "\r\n" );
document.write( "Carry all calculations to 7 significant figures. (show work)\r\n" );
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document.write( "       (1)[1 - (1/3)12]\r\n" );
document.write( "S10 = ------------------\r\n" );
document.write( "           1 - 1/3\r\n" );
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document.write( "       1 - 1/312\r\n" );
document.write( "S10 = ----------- \r\n" );
document.write( "          2/3    \r\n" );
document.write( "\r\n" );
document.write( "Punching that out on my TI-84\r\n" );
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document.write( "(1-1/3^12)/(2/3) ENTER\r\n" );
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document.write( "get .6666654122\r\n" );
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document.write( "or to 7 figures, .6666654\r\n" );
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document.write( "d. What observation can make about the successive partial \r\n" );
document.write( "sum of this series? In particular, what number does it \r\n" );
document.write( "appear that the sum will always be smaller than?\r\n" );
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document.write( "It appears that we get more and more 6's, and so it appears \r\n" );
document.write( "that the sum will always be smaller than .666666666666666... \r\n" );
document.write( "where the 6's go on forever. We know that this repeating \r\n" );
document.write( "decimal is equivalent to 2/3.  So it appears that the sum \r\n" );
document.write( "will always be less than 2/3.\r\n" );
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document.write( "Edwin
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