Question

(ii) 3, 9, 27, 81, ...

Answer 1

$$\begin{gathered} \left(\mathrm{ii}\right)\mathrm{In}\mathrm{the}\mathrm{given}\mathrm{sequence},\mathrm{we}\mathrm{have}: \\ {t}_1=3,t_2=9,t_3=27\mathrm{and}{t}_4=81 \\ \mathrm{Thus},\mathrm{we}\mathrm{get}: \\ {t}_1=3=3^1 \\ {t}_2=9=3^2 \\ {t}_3=27=3^3 \\ {t}_4=81=3^4 \\ \Rightarrow t_n=3^n \\ \mathrm{Now},\mathrm{to}\mathrm{find}\mathrm{the}\mathrm{next}\mathrm{four}\mathrm{terms},\mathrm{we}\mathrm{need}\mathrm{to}\mathrm{take}n=5,6,7\mathrm{and}8. \\ \mathrm{We}\mathrm{get}: \\ {t}_5=3^5=243 \\ {t}_6=3^6=729 \\ {t}_7=3^7=2187 \\ {t}_8=3^8=6561 \\ \mathrm{Thus},\mathrm{the}\mathrm{next}\mathrm{four}\mathrm{terms}\mathrm{are}243,729,2187\mathrm{and}6561. \end{gathered}$$