Question 986777
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For a given geometric sequence,  whose terms all are positive real numbers,

{{{a[1]}}} = {{{2/3}}}  and  {{{a[5]}}} = {{{1/24}}}.  Find {{{a[6]}}}.
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{{{a[5]/a[1]}}} = {{{q^4}}} = {{{1/24}}}:{{{2/3}}} = {{{3/(24*2)}}} = {{{1/16}}}.


Hence,  {{{q}}} = {{{root(4,1/16)}}} = {{{1/2}}}       (Notice that negative q does't fit, because all terms should be positive).


It implies that  {{{a[6]}}} = {{{a[5]}}}.{{{1/2}}} = {{{1/24}}}.{{{1/2}}} = {{{1/48}}}. 


<B>Answer</B>. &nbsp;{{{a[6]}}} = {{{1/48}}}.