Question 818503
a, ar, ar^2, ar^3 are the terms.


{{{a+ar^3=27}}} and {{{ar+ar^2=18}}}


Note that {{{a(1+r^2)=27}}} and {{{(ar+r)(1+r)=18}}} or {{{r(a+1)(1+r)=18}}};
Also {{{a+ar+ar^2+ar^3=39}}}


One task might be solve {{{a(1+r^2)=27}}} for a, and solve {{{r(a+1)(1+r)=18}}} for r;  and then you can get an expression for the term ar and you can also get a value for {{{ar}}}.


Ordinarily, I would solve a help-requested problem at least partially or give a more complete strategy.  I won't this time.  Can what I gave so far help with this problem?  What I'm doing here is not the best way, but might be enough for you to make progress with the question.