document.write( "Question 1196057: Find the general rule of the sequence: 32, -16, 8, -4, ... \n" ); document.write( "
Algebra.Com's Answer #828750 by math_tutor2020(3817)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "Without more info, there could be infinitely many possible answers. See my previous post here for more details.\r
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\n" ); document.write( "\n" ); document.write( "If we assume the sequence is geometric, then,
\n" ); document.write( "a = 32 = first term
\n" ); document.write( "r = -1/2 = common ratio
\n" ); document.write( "The idea is to multiply each term by -1/2\r
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\n" ); document.write( "\n" ); document.write( "which leads to,
\n" ); document.write( "nth term = a*( r )^(n-1)
\n" ); document.write( "nth term = 32*( -1/2 )^(n-1)
\n" ); document.write( "Again this all hinges on the assumption we have a geometric sequence. \r
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\n" ); document.write( "\n" ); document.write( "Let's check the answer with something like n = 3
\n" ); document.write( "a_n = 32*(-1/2)^(n-1)
\n" ); document.write( "a_3 = 32*(-1/2)^(3-1)
\n" ); document.write( "a_3 = 32*(-1/2)^(2)
\n" ); document.write( "a_3 = 32*(1/4)
\n" ); document.write( "a_3 = 8
\n" ); document.write( "We have 8 as the third term, which indeed matches with the given sequence. I'll let you check the other values.
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