document.write( "Question 326512: the sum of the 1st and 2nd term of a geometric progression is 10 while its sum to infinity is 18. find the fourth term \n" ); document.write( "

Algebra.Com's Answer #233836 by galactus(183) $\"\"$ $\"About$

You can put this solution on YOUR website!
The infinite sum is given by $\"a1%2F%281-r%29=18\"$ \r
\n" ); document.write( "\n" ); document.write( "The nth partial sum is given by $\"a1%28%281-r%5En%29%2F%281-r%29%29\"$ \r
\n" ); document.write( "\n" ); document.write( "Since we are told the first 2 terms sum to 10, then we have \r
\n" ); document.write( "\n" ); document.write( " $\"a1%28%281-r%5E2%29%2F%281-r%29%29=10\"$ \r
\n" ); document.write( "\n" ); document.write( "But, from the first equation, $\"a1=18%281-r%29\"$ \r
\n" ); document.write( "\n" ); document.write( "Sub into the second equation:\r
\n" ); document.write( "\n" ); document.write( " $\"18%281-r%29%28%281-r%5E2%29%2F%281-r%29%29=10\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"r=2%2F3\"$ \r
\n" ); document.write( "\n" ); document.write( "and the first term, a1, is\r
\n" ); document.write( "\n" ); document.write( " $\"18%281-2%2F3%29=6\"$ \r
\n" ); document.write( "\n" ); document.write( "Since the nth term is gven by $\"a1%2Ar%5E%28n-1%29\"$ , \r
\n" ); document.write( "\n" ); document.write( "The fourth term is\r
\n" ); document.write( "\n" ); document.write( " $\"6%2A%282%2F3%29%5E3=16%2F9\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );