document.write( "Question 536481: The 3rd and 5th term of a G.P are 25 and 100 respectively.Find the 7th term of the G.P
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Algebra.Com's Answer #352388 by Edwin McCravy(20086)\"\" \"About 
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3rd and 5th term of a G.P are 25 and 100 respectively. Find the 7th term:
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document.write( "    ___, ___,  25, ___, 100, ___,  ? \r\n" );
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document.write( "We could use formulas but the easiest way is \r\n" );
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document.write( "1. Let r = the common ratio,\r\n" );
document.write( "2. the 4th term has to equal the 3rd term, 25, times r. So fill in the\r\n" );
document.write( "   3rd term as 25r:\r\n" );
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document.write( "    ___, ___,  25, 25r, 100, ___,  ? \r\n" );
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document.write( "3. Then the 5th term has to equal the 4th term, 25r, times r. \r\n" );
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document.write( "4. Get the equation from \r\n" );
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document.write( "                          \"%28matrix%282%2C1%2C4th%2C+term%29%29\"×r = \"%28matrix%282%2C1%2C5th%2C+term%29%29\"\r\n" );
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document.write( "                           (25r)r = 100\r\n" );
document.write( "                             25r² = 100\r\n" );
document.write( "                               r² = 4\r\n" );
document.write( "                                r = ±2\r\n" );
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document.write( "Aha!  There are two solutions for r, so we will use ±r for both:\r\n" );
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document.write( "5. Get the 6th term by multiplying the 5th term, 100 by ±2 getting ±200  \r\n" );
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document.write( "    ___, ___,  25, 25r, 100, ±200,  ? \r\n" );
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document.write( "6. Get the 7th term by multiplying the 6th term, ±200, by ±2, and\r\n" );
document.write( "regardless of whether r=+2 or r=-2, the 7th term will be +400\r\n" );
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document.write( "    ___, ___,  25, 25r, 100, ±200, 400\r\n" );
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document.write( "If we like we can get the whole progressions:\r\n" );
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document.write( "One way the progression could be is this:\r\n" );
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document.write( "    6.25,  12.5, 25,  50, 100,  200, 400\r\n" );
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document.write( "and the other way is\r\n" );
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document.write( "    6.25, -12.5, 25, -50, 100, -200, 400\r\n" );
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document.write( "But either way the 7th term is 400.\r\n" );
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document.write( "Edwin
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