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\n" ); document.write( "Technically, the question can't be answered, because any next number(s) would form a valid sequence, and obviously different subsequent numbers would require different forms of the formula for the n-th term.
\n" ); document.write( "But in this example it is fairly clear what the intended sequence is.
\n" ); document.write( "To see the pattern and be able to write a formula for the n-th term, notice the denominators of the terms: 27, 3, 3, 1. Then rewrite the second term as an equivalent fraction with denominator 9, so that the denominators are decreasing powers of 3:
\n" ); document.write( "-1/27, 3/9, -5/3, 7/1
\n" ); document.write( "Now we have a clear pattern:
\n" ); document.write( "(1) alternating signs, with first term negative
\n" ); document.write( "To get that, we need a factor of
\n" ); document.write( "(2) numerator (ignoring the alternating signs): consecutive odd numbers starting with 1
\n" ); document.write( "For that, we need a factor of
\n" ); document.write( "(3) denominator: powers of 3, starting with 3 for the first term and decreasing by 1
\n" ); document.write( "For that, we need a factor of
\n" ); document.write( "ANSWER:
\n" ); document.write( " \n" ); document.write( "