document.write( "Question 150298: Please help me solve the following:
\n" ); document.write( "Which of the following describes the sequence:
\n" ); document.write( "5, (-5/3), (5/9), (-5/27), (5/81), ...
\n" ); document.write( "The answer choices are:
\n" ); document.write( "1. Geometric, r=(-1/3)
\n" ); document.write( "2. Arithmetic, d=(-1/3)
\n" ); document.write( "3. Geometric, r=(1/3)
\n" ); document.write( "4. Arithmetic, d=(-5/6)
\n" ); document.write( "Thank you, Ray \n" ); document.write( "

Algebra.Com's Answer #110396 by Edwin McCravy(20056) $\"\"$ $\"About$

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Please help me solve the following:
\n" ); document.write( "Which of the following describes the sequence:
\n" ); document.write( "5, (-5/3), (5/9), (-5/27), (5/81), ...
\n" ); document.write( "The answer choices are:
\n" ); document.write( "1. Geometric, r=(-1/3)
\n" ); document.write( "2. Arithmetic, d=(-1/3)
\n" ); document.write( "3. Geometric, r=(1/3)
\n" ); document.write( "4. Arithmetic, d=(-5/6)
\n" ); document.write( "Thank you, Ray
\n" ); document.write( "

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document.write( "To find out if a sequence is arithmetic when given 4 terms:\r\n" );
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document.write( "1. Subtract 2nd term minus 1st term.\r\n" );
document.write( "2. Subtract 3rd term minus 2nd term.\r\n" );
document.write( "3. Subtract 4th term minus 3rd term.\r\n" );
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document.write( "If all three are the same then the sequence is arithmetic,\r\n" );
document.write( "with d = common difference = this value.\r\n" );
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document.write( "To find out if a sequence is geometric when given 4 terms:\r\n" );
document.write( "1. Divide 2nd term by 1st term.\r\n" );
document.write( "2. Divide 3rd term by 2nd term.\r\n" );
document.write( "3. Divide 4th term by 3rd term.\r\n" );
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document.write( "If all three are the same then the sequence is geometric,\r\n" );
document.write( "with r = common ratio = this value.\r\n" );
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document.write( "-----------------------\r\n" );
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document.write( "First we test to see if it's an arithmetic sequence:\r\n" );
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document.write( "1. Subtract 2nd term minus 1st term.  (5/9) - (-5/3) = 20/9  \r\n" );
document.write( "2. Subtract 3rd term minus 2nd term. (-5/27) - (5/9) = -20/27 \r\n" );
document.write( "3. No need to subtract 4th term minus 3rd term since those aren't the\r\n" );
document.write( "  same.  We know it is not an arithmetic sequence.\r\n" );
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document.write( "So that rules out choices 2 and 4.  So it's between 1 and 3.\r\n" );
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document.write( "Next we test to see if it's a geometric sequence:\r\n" );
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document.write( "1. Divide 2nd term by 1st term.  (5/9)÷(-5/3) = (5/9)(-3/5) = -1/3\r\n" );
document.write( "2. Divide 3rd term by 2nd term.  (-5/27)÷(5/9)= (-5/27)(9/5) = -1/3\r\n" );
document.write( "3. Divide 4th term by 3rd term.  (5/81)÷(-5/27) = (5/81)(-27/5) = -1/3 \r\n" );
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document.write( "All three are the same, so the sequence is geometric,\r\n" );
document.write( "with r = -1/3.\r\n" );
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document.write( "The correct choice is 1.\r\n" );
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document.write( "Edwin

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