document.write( "Question 970124: If in a geometric progression,the second term exceeds the first term by 20 and the fourth term exceeds the second term by 15,find the possible values of the first term. \n" ); document.write( "

Algebra.Com's Answer #592798 by reviewermath(1029) $\"\"$ $\"About$

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If in a geometric progression,the second term exceeds the first term by 20 and the fourth term exceeds the second term by 15,find the possible values of the first term.
\n" ); document.write( "Solution:
\n" ); document.write( "Let x = first term of a geometric progression and r = common ratio.
\n" ); document.write( "The terms of a geometric progression in terms of x and r are
\n" ); document.write( "x, xr, $\"xr%5E2\"$ , $\"xr%5E3\"$ , ...
\n" ); document.write( "Therefore,
\n" ); document.write( "xr - x = 20 and $\"xr%5E3\"$ - xr = 15
\n" ); document.write( " $\"x+=+20%2F%28r-1%29\"$ and $\"x+=+15%2F%28r%5E3-r%29\"$
\n" ); document.write( " $\"20%2F%28r-1%29+=+15%2F%28r%5E3-r%29\"$
\n" ); document.write( " $\"20%28r%5E3-r%29+=+15%28r-1%29\"$
\n" ); document.write( " $\"20r%5E3-35r%2B15=0\"$
\n" ); document.write( "5(r-1)(2r-1)(2r+3) = 0
\n" ); document.write( "r = 1, 1/2, -3/2
\n" ); document.write( "If r = 1, then x is undefined
\n" ); document.write( "If r = 1/2, then x= $\"20%2F%281%2F2-1%29+=+-40\"$
\n" ); document.write( "If r = -3/2, then x = $\"20%2F%28-3%2F2-1%29+=+-8\"$
\n" ); document.write( "Answer: -40 or -8 \n" ); document.write( "

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