Mathematics - Sequence & Series Question with Solution | TestHub

$a_1+a_2=4\Rightarrow a_1+a_{1}r=4\dots \left(1\right)$

$a_3+a_4=16\Rightarrow a_1{r}^2+a_1{r}^3=16\dots \left(2\right)$

$\frac{1}{r^2}=\frac{1}{4}\Rightarrow r^2=4 \Rightarrow r=-2 \left(a_1<0\right)$

$\sum _{i=1}^a{a}_i=\frac{a_1\left(r^9-1\right)}{r-1}=\frac{\left(-4\right)\left[{\left(-2\right)}^9-1\right]}{\left(-2-1\right)}=\frac{4}{3}\left(-513\right)=4\lambda$

$\lambda =-171$.