Question

Please I need help with this ASAP​

Answer 1

`\bf \begin{array}{ccll} term&value\\ \cline{1-2} s_4&18\\ s_5&18r\\ s_6&18rr\\ &18r^2 \end{array}\qquad \qquad \stackrel{s_6}{8}=18r^2\implies \cfrac{8}{18}=r^2\implies \cfrac{4}{9}=r^2 \\\\\\ \sqrt{\cfrac{4}{9}}=r\implies \cfrac{√(4)}{√(9)}=r\implies \boxed{\cfrac{2}{3}=r} \\\\[-0.35em] ~\dotfill`

`\bf n^(th)\textit{ term of a geometric sequence} \\\\ s_n=s_1\cdot r^(n-1)\qquad \begin{cases} s_n=n^(th)\ term\\ n=\textit{term position}\\ s_1=\textit{first term}\\ r=\textit{common ratio}\\ \cline{1-1} n=6\\ s_6=8\\ r=(2)/(3) \end{cases}\implies 8=s_1\left( (2)/(3) \right)^(6-1) \\\\\\ 8=s_1\left( (2)/(3) \right)^5\implies 8=s_1\cdot \cfrac{32}{243}\implies 8\cdot \cfrac{243}{32}=s_1\implies \boxed{\cfrac{243}{4}=s_1}`