document.write( "Question 753894: The third and sixth terms of a geometric sequence are -75 and -9375 respectively. Find the first term, the common ratio, and an explicit rule for the nth term \n" ); document.write( "

Algebra.Com's Answer #459381 by htmentor(1343) $\"\"$ $\"About$

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The formula for the n-th term of a geometric sequence is
\n" ); document.write( " $\"a%28n%29+=+ar%5E%28n-1%29\"$ where a = the first term, and r is the common ratio
\n" ); document.write( "We are given 3rd and 6th terms:
\n" ); document.write( " $\"a%283%29+=+ar%5E2+=+-75+-%3E+a+=+-75%2Fr%5E2\"$
\n" ); document.write( " $\"a%286%29+=+ar%5E5+=+-9375+-%3E+%28-75%2Fr%5E2%29r%5E5+=+-75r%5E3\"$
\n" ); document.write( "Solve for r:
\n" ); document.write( " $\"r%5E3+=+-9375%2F-75+=+125+-%3E+r+=+5\"$
\n" ); document.write( "Since $\"a%283%29+=+ar%5E2+=+a%285%29%5E2+=+-75\"$ this means that the first term, a = -75/25 = -3
\n" ); document.write( "The rule for the nth term is $\"a%28n%29+=+-3%2A5%5E%28n-1%29\"$
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