Question 891682
It looks like each successive number is multiplied by {{{-1/3}}}
2nd term : {{{-(9/2)(-1/3)=3/2}}}
3rd term : {{{(3/2)(-1/3)=-1/2}}}
4th term : {{{-(1/2)(-1/3)=1/6}}}
So then, continuing on,
{{{1/39366}}} would be the 12th term.
The constant term would be,
{{{a(-1/3)=-9/2}}}
{{{a=27/2}}}
So then, the series would look like,
{{{A[n]=(27/2)(-1/3)^n}}}
The sum would then be,
{{{S[n]=(-9/2)(((1-(-1/3)^n))/(1-(-1/3)))}}}
{{{S[n]=(-9/2)(((1-(-1/3)^n))/(4/3))}}}

{{{S[n]=(-9/2)(3/4)(1-(-1/3)^n)}}}
{{{S[n]=(-27/8)(1-(-1/3)^n)}}}
So for {{{n=12}}}
{{{S[12]=(-27/8)(1-(-1/3)^12)}}}
{{{S[12]=(-27/8)(1-1/531441)}}}
{{{highlight(S[12]=-27/8)}}}