document.write( "Question 1179300: A rubber ball is dropped from a height of 100 feet, and at each bounce it rebounds one-half of the height from which it last fell. What distance has the ball traveled up to the instant it hits the ground for the eight time? Solve using a geometric sequence. \n" ); document.write( "
Algebra.Com's Answer #808966 by Boreal(15235)\"\" \"About 
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First time, it drops 100 feet
\n" ); document.write( "Then it rises 50 and drops 50 for second time and so forth.
\n" ); document.write( "100+(100)(1/2)+100(1/2) for the second, and we only care about the distance traveled, not the direction.
\n" ); document.write( "100+100(1/2)+100(1/2)+100(1/2)^2+100(1/2)^2 +...+100(1/2)^7+100(1/2)^7.
\n" ); document.write( "Leave out the first term for a moment.
\n" ); document.write( "the other terms are 200(1/2)+200(1/2)^2+200(1/2)^3+200(1/2)^4+200(1/2)^5+200(1/2)^6+200(1/2)^7
\n" ); document.write( "The geometric sequence for sum of (1/2)^n for n=1-7 is a*(1-r^n)/(1-r); a, the first term, is 100
\n" ); document.write( "This is here 100(1-(1/128))/(1/2)
\n" ); document.write( "This is 100(63/64)*2=400*63/64=198.4375 feet
\n" ); document.write( "Now bring in the other term 100 for the first drop, and the answer is 298.4375 feet.\r
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\n" ); document.write( "\n" ); document.write( "Check this
\n" ); document.write( "down 100
\n" ); document.write( "up 50 down 50 (100)
\n" ); document.write( "up 25 down 25 (50)
\n" ); document.write( "up 12.5 down 12.5 (25)
\n" ); document.write( "then 12.5
\n" ); document.write( "then 6.25
\n" ); document.write( "then 3.125
\n" ); document.write( "then 1.5625
\n" ); document.write( "That sum is 298.4375 feet\r
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