Question

Find the 4th term from the end of the G.P. $\frac{1}{2},\frac{1}{6},\frac{1}{18},\frac{1}{54},...,\frac{1}{4374}$

Answer 1

$$\begin{gathered} \mathrm{After}\mathrm{reversing}\mathrm{the}\mathrm{given}\mathrm{G}.\mathrm{P}.,\mathrm{we}\mathrm{get}\mathrm{another}\mathrm{G}.\mathrm{P}.\mathrm{whose}\mathrm{first}\mathrm{term},l\mathrm{is}\frac{1}{4374}\mathrm{and}\mathrm{common}\mathrm{ratio}\mathrm{is}3. \\ \therefore 4^{\mathrm{th}}\mathrm{term}\mathrm{from}\mathrm{the}\mathrm{end}=l{\left(\frac{1}{r}\right)}^{4-1} \\ =\left(\frac{1}{4374}\right){\left(3\right)}^{4-1} \\ =\left(\frac{27}{4374}\right) \\ =\frac{1}{162} \end{gathered}$$