document.write( "Question 336304: a G.P has a first term of a, a common ratio of r and its 6th term is 768. another G.P has a first term of a, a common ratio of 6r and its 3rd term is 3456. evaluate a and r. \n" ); document.write( "
Algebra.Com's Answer #241097 by galactus(183)\"\" \"About 
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The nth term of a geometric sequence is given by \r
\n" ); document.write( "\n" ); document.write( "\"an=a1%2Ar%5E%28n-1%29\"\r
\n" ); document.write( "\n" ); document.write( "For the first condition, the 6th term is 768:\r
\n" ); document.write( "\n" ); document.write( "\"a6=a1%2Ar%5E5=768\"\r
\n" ); document.write( "\n" ); document.write( "For the second condition, the third term is 3456:\r
\n" ); document.write( "\n" ); document.write( "\"a3=a1%2A36r%5E2=3456\"\r
\n" ); document.write( "\n" ); document.write( "So, we have two equations with two unknowns to solve, a and r:\r
\n" ); document.write( "\n" ); document.write( "\"a1%2Ar%5E5=768\"
\n" ); document.write( "\"a1%2Ar%5E2=96\"\r
\n" ); document.write( "\n" ); document.write( "Solve the first one for \"a1=768%2Fr%5E5\" and sub into the second one:\r
\n" ); document.write( "\n" ); document.write( "\"%28768%2Fr%5E5%29%2Ar%5E2=96\"\r
\n" ); document.write( "\n" ); document.write( "\"768%2Fr%5E3=96\"\r
\n" ); document.write( "\n" ); document.write( "\"r=2\"\r
\n" ); document.write( "\n" ); document.write( "Therefore, \"a1=24\"
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