document.write( "Question 862286: A geometric sequence has a term of a4= –54 and a common ratio of r = 3. What is the rule for the nth term? \n" ); document.write( "
Algebra.Com's Answer #519603 by Theo(13342)\"\" \"About 
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A4 = -54
\n" ); document.write( "r = 3
\n" ); document.write( "The formula is:
\n" ); document.write( "An = A1 * r^(n-3)
\n" ); document.write( "Since you have A4 and r, you can solve for A1.
\n" ); document.write( "the formula is:
\n" ); document.write( "A4 = A1 * r^(4-1)
\n" ); document.write( "replace variable with their known values and you get:
\n" ); document.write( "-54 = A1 * 3^(3)
\n" ); document.write( "simplify this to get:
\n" ); document.write( "-54 = A1 * 27
\n" ); document.write( "divide both sides of this equation by 27 to get:
\n" ); document.write( "-54/27 = A1 which makes A1 = -2.
\n" ); document.write( "Now that you have A1, you can apply the formula to get the nth term.
\n" ); document.write( "The formula is An = A1 * r^(n-1)
\n" ); document.write( "replace A1 with -2 and r with 3 to get:
\n" ); document.write( "An = -2 * 3^(n-1)
\n" ); document.write( "If n is equal to 4, then this formula will get you:
\n" ); document.write( "A4 = -2 * 3^(3) which will get you A4 = -2 * 27 which will get you A4 = -54.
\n" ); document.write( "we're back where we started, which is good because the formula works for n = 4 and will also work for n = any other number.
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