Question

A geometric sequence has four positive terms $a_1,a_2,a_3,a_4$. If $\frac{a_3}{a_1}=9$ and $a_1+a_2=\frac{4}{3}$, then $a_4$ equals

• A. 3
• B. 9
• C. 27
• D. $3\sqrt{3}$

Answer 1

Answer: (B)

$\frac{a{r}^2}{a}=9\Rightarrow r=3$
$a+ar=\frac{4}{3}\therefore a\cdot 4=\frac{4}{3}\Rightarrow a=\frac{1}{3}$
$\therefore a_4=a{r}^3=\frac{1}{3}\cdot 3^3=3^2=9$