Question 1025107
<pre>
To find the common ratio, r,

{{{matrix(1,2,common,ratio)}}}{{{""=""}}}{{{matrix(1,2,second,term)/matrix(1,2,first,term)}}}{{{""=""}}}{{{matrix(1,2,third,term)/matrix(1,2,second,term)}}}{{{""=""}}}{{{r}}}

33,12/1,48/11

{{{matrix(1,2,second,term)/matrix(1,2,first,term)}}}{{{""=""}}}{{{matrix(1,22,

12/1,"÷",33,"",""="","",12/1,"÷",33/1,"",""="","",12/1,"×",1/33,"",""="",
"",12/33,"",""="",4/11)}}}

{{{matrix(1,2,third,term)/matrix(1,2,second,term)}}}{{{""=""}}}{{{matrix(1,16,

48/11,"÷",12/1,"",""="","",48/11,"÷",1/12,"",""="","",48/(11*12),"",""="",4/11)}}}

{{{r}}}{{{""=""}}}{{{4/11}}}

{{{matrix(1,3,
a[n],""="",(a[1](1-r^n))/(1-r))}}}

{{{matrix(1,3,
a[n],""="",((33)(1-(4/11)^n))/(1-(4/11)))}}}

{{{matrix(1,3,
a[n],""="",((33)(1-(4/11)^n))/(11/11-4/11))}}}


{{{matrix(1,3,
a[n],""="",((33)(1-(4/11)^n))/(7/11))}}}

{{{matrix(1,3,
a[n],""="",((33)(1-(4/11)^n))*(11/7))}}}

{{{matrix(1,3,
a[n],""="",(33*11/7)(1-(4/11)^n))}}}

{{{matrix(1,3,
a[n],""="",(3*11*11/7)(1-(4^n/11^n)^""))}}}

{{{matrix(1,3,
a[n],""="",(3*11^2/7^"")(1-(4^n/11^n)^""))}}}

{{{matrix(1,3,
a[n],""="",expr(3/7)(11^2)(1-(4^n/11^n)^""))}}}

{{{matrix(1,3,
a[n],""="",expr(3/7)((11^2)-(11^2)(4^n/11^n)^""))}}}

{{{matrix(1,3,
a[n],""="",expr(3/7)(121-4^n/11^(n-2)))}}}

{{{a[10]}}}{{{""=""}}}{{{11115589725/214358881}}}

approximately 51.85504642095981085103723787399319368531318280206920841315...

Edwin</pre>