3.

Tentukan rumus suku ke n dan suku ke 8 dari barisan geometri di bawah ini ?

 a. $8$, $2$, $\frac{1}{2}$ , $\frac{1}{8}$, $....$ b. $\frac{2}{9}$, $-\frac{2}{3}$, $2$, $-6$, $...$

##### J A W A B
 a. $8$, $2$, $\frac{1}{2}$ , $\frac{1}{8}$, $....$ Suku pertamanya $a=8$ dan rasionya $r=\frac{{U}_{2}}{{U}_{1}}=\frac{2}{8}=\frac{1}{4}$ ${U}_{n}=a{r}^{n-1}$ $\to$ ${U}_{n}=8{\left(\frac{1}{4}\right)}^{n-1}$ ${U}_{8}=a{r}^{7}$ $=8{\left(\frac{1}{4}\right)}^{7}$ $=\frac{{2}^{3}}{{2}^{14}}$ $=\frac{1}{{2}^{11}}$ $=\frac{1}{2048}$ b. $\frac{2}{9}$, $-\frac{2}{3}$, $2$, $-6$, $...$ Suku pertamanya $a=\frac{2}{9}$ dan rasionya $r=\frac{{U}_{4}}{{U}_{3}}=\frac{-6}{2}=-3$ ${U}_{n}=a{r}^{n-1}$ $\to$ ${U}_{n}=\frac{2}{9}{\left(-3\right)}^{n-1}$ ${U}_{8}=a{r}^{7}$ $=\frac{2}{9}×{\left(-3\right)}^{7}$ $=\frac{-2×{3}^{7}}{{3}^{2}}$ $=-2×{3}^{5}$ $=-486$