Question

What is the explicit formula for the geometric sequence 224,112.56,28

Answer 1

`224~~,~~\stackrel{224\cdot (1)/(2)}{112}~~,~~\stackrel{112\cdot (1)/(2)}{56}~~,~~\stackrel{56\cdot (1)/(2)}{28}~~,~~...\hspace{5em}\stackrel{\textit{common ratio}}{r=\cfrac{1}{2}} \\\\[-0.35em] ~\dotfill`

`n^(th)\textit{ term of a geometric sequence} \\\\ a_n=a_1\cdot r^(n-1)\qquad \begin{cases} a_n=n^(th)\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ r=\textit{common ratio}\\[-0.5em] \hrulefill\\ a_1=224\\ r=(1)/(2) \end{cases}\qquad \implies\qquad a_n=224\left( (1)/(2) \right)^(n-1)`