Question

In a G.P. if $t_3=2$ and $t_6=-\frac{1}{4},$ then $t_{10}=$

• A. $-\frac{1}{128}$
• B. $-\frac{1}{64}$
• C. $\frac{1}{128}$
• D. $\frac{1}{64}$

Answer 1

The correct option is B $-\frac{1}{64}$

$t_3=2,t_6=-\frac{1}{4}$
$a{r}^2=2,a{r}^5=-\frac{1}{4}$
$\Rightarrow \frac{1}{r^3}=-8$
$\Rightarrow r=-\frac{1}{2}$
$\Rightarrow a=8$
$t_{10}=a{r}^9=8{\left(\frac{-1}{2}\right)}^9=\frac{-1}{64}$