Question 925143
First term, a.
Index, n.
ratio between terms, r.
{{{a*r=8}}}, also {{{a*r^(2-1)=8}}} or {{{a*r^(n-1)=TheGeneralTerm}}}.


The seventh term, {{{ar^(7-1)=0.25}}}.
{{{a*r^6=0.25}}}


Two equations should be useful.
{{{system(ar=8,ar^6=(1/4))}}}


Their ratio should be very helpful.
{{{(ar^6)/(ar)=(1/4)/8}}}
{{{r^5=1/32}}}
{{{r^5=1/2^5}}}
{{{r^5=(1/2)^5}}}
{{{highlight(r=1/2)}}}


Having the common ratio, the factor a can be found.
{{{a*(1/2)=8}}}
{{{a=16}}}


The general term of the geometric sequence is {{{highlight(16*(1/2)^((n-1)))}}}.


If the formula for a finite series is being handled properly,  expect sum of first ten terms,
{{{16(1-(1/2)^10)/(1-1/2)}}}, and you can evaluate the expression.


{{{16(1-1/1024)*2}}}


and this is slightly less than 32.