Question

Please help me with this. I am stuck on this like glue on this problem​

Answer 1

$\bf \begin{array}{ccll} term&value\\ \cline{1-2} s_5&10\\ s_6&10r\\ s_7&10rr\\ s_8&10rrr\\ &10r^3 \end{array}\qquad \qquad \stackrel{s_8}{80}=10r^3\implies \cfrac{80}{10}=r^3\implies 8=r^3 \\\\\\ \sqrt[3]{8}=r\implies \boxed{2=r} \\\\[-0.35em] ~\dotfill$

$\bf n^{th}\textit{ term of a geometric sequence} \\\\ s_n=s_1\cdot r^{n-1}\qquad \begin{cases} s_n=n^{th}\ term\\ n=\textit{term position}\\ s_1=\textit{first term}\\ r=\textit{common ratio}\\ \cline{1-1} n=8\\ s_8=80\\ r=2 \end{cases}\implies 80=s_1(2)^{8-1} \\\\\\ 80=s_1(2)^7\implies \cfrac{80}{2^7}=s_1\implies \cfrac{80}{128}=s_1\implies \boxed{\cfrac{5}{8}=s_1}$