Question 979571


Since we are given the geometric progression,  we have


{{{a[1]}}} = {{{1/2}}}, 


{{{a[9]}}} = {{{a[1]*r^(9-1)}}} = {{{a[1]*r^8}}} = {{{64}}},


where &nbsp;{{{r}}}&nbsp; is the &nbsp;<B><U>common ratio</U></B>&nbsp; of the progression.


It implies that &nbsp;{{{r^8}}} = {{{a[9]/a[1]}}} = {{{64}}}:{{{1/2}}} = {{{128}}} = {{{2^7}}}. 



Hence, &nbsp;{{{r}}} = {{{root(8, 2^7)}}} = {{{2^(7/8)}}} = 2^(7/8).