document.write( "Question 1202408: The third term of a geometric progression is nine times the first term. The sum of the first six terms is k times the sum of the first two terms. Find the value of k. \n" ); document.write( "

Algebra.Com's Answer #837223 by ikleyn(52928) $\"\"$ $\"About$

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\n" ); document.write( "The third term of a geometric progression is nine times the first term.
\n" ); document.write( "The sum of the first six terms is k times the sum of the first two terms. Find the value of k.
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document.write( " =  +  +  +  +  + .\r\n" );
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document.write( "Group the terms\r\n" );
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document.write( " = () + () + ().\r\n" );
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document.write( "You are given   = .\r\n" );
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document.write( "It implies   = ;   = ;   = .\r\n" );
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document.write( "Therefore\r\n" );
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document.write( " =  +  +  =  = .\r\n" );
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document.write( "Thus the coefficient k is equal to 91.\r\n" );
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document.write( "ANSWER.  k = 91.\r\n" );
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\n" ); document.write( "\n" ); document.write( "On geometric progressions, see introductory lessons\r
\n" ); document.write( "\n" ); document.write( "    - Geometric progressions\r
\n" ); document.write( "\n" ); document.write( "    - The proofs of the formulas for geometric progressions \r
\n" ); document.write( "\n" ); document.write( "    - Problems on geometric progressions\r
\n" ); document.write( "\n" ); document.write( "    - Word problems on geometric progressions\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Learn the subject from there.\r
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