Answer :
We have a Geometric Progression and this means that any term differs from its preliminary and subsequent terms by a ratio that will be represented below:
[tex]\begin{gathered} T_n=ar^{n-1} \\ \text{where:} \\ T_n=\text{Arbitrary Term} \\ a=\text{ First term} \\ r\text{ = common ratio} \\ n=\text{ordinal of the term} \end{gathered}[/tex]In our question, we are asked to find the 2nd term and 3rd term, we're to find T when n is 2 and 3.
First though, we need to find ratio, r
[tex]\begin{gathered} a=243 \\ T_4=ar^3=243\times r^3 \\ -9=243\times r^3 \\ r^3=-\frac{9}{243}=-\frac{1}{27} \\ \text{Getting the 3rd roots of both sides gives:} \\ r=-\frac{1}{3} \end{gathered}[/tex]Having gotten our value of r, we proceed to find the 2nd term and 3rd terms with the formulae
[tex]\begin{gathered} T_2=ar^{2-1}=ar \\ T_2=243\times(\frac{-1}{3})^{}=-81 \end{gathered}[/tex][tex]\begin{gathered} T_3=ar^{3-1}=ar^2 \\ T_2=243\times(\frac{-1}{3})^2=27 \end{gathered}[/tex]Therefore,
2nd Term = -81
3rd Term = 27