document.write( "Question 1020019: Please help me solve these question, in geometric progression. The first and the last term of the geometric progression are 2 and 2,048 respectively.The sum of the term of the progression is 2,730 find the number of terms and the common ratio (c.r) \n" ); document.write( "

Algebra.Com's Answer #635986 by robertb(5830) $\"\"$ $\"About$

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The first term $\"g%5B1%5D+=+2\"$ , the nth term is $\"g%5Bn%5D\"$ = 2,048.
\n" ); document.write( "The sum of the first n terms of a geometric sequence is given by the formula \r
\n" ); document.write( "\n" ); document.write( " $\"S%5Bn%5D+=+%28g%5B1%5D+-+g%5Bn%5D%2Ar%29%2F%281-r%29\"$ \r
\n" ); document.write( "\n" ); document.write( "After substitution, \r
\n" ); document.write( "\n" ); document.write( " $\"2730+=+%282-2048r%29%2F%281-r%29\"$ \r
\n" ); document.write( "\n" ); document.write( "<==> 2730 - 2730r = 2 - 2,048r, after cross-multiplying.
\n" ); document.write( "<==> 2,728 = 682r
\n" ); document.write( "<==> $\"highlight%28r+=+4%29\"$ , the common ratio (c.r.)\r
\n" ); document.write( "\n" ); document.write( "Now from the formula for the nth term of a gp, $\"g%5Bn%5D+=+g%5B1%5D%2Ar%5E%28n-1%29\"$ ,\r
\n" ); document.write( "\n" ); document.write( "we get\r
\n" ); document.write( "\n" ); document.write( " $\"2048+=+2%2A4%5E%28n-1%29\"$ , and we proceed to determine the value of n.
\n" ); document.write( "<==> $\"1024+=+4%5E%28n-1%29+=+2%5E%282n-2%29\"$
\n" ); document.write( "==> $\"log%282%2C1024%29+=+log%282%2C2%5E%282n-2%29%29\"$
\n" ); document.write( "==> 10 = 2n - 2
\n" ); document.write( "==> 12 = 2n
\n" ); document.write( "==> $\"highlight%28n+=+6%29\"$ , the number of terms added in the sequence,
\n" ); document.write( "and the problem is solved. \n" ); document.write( "

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