Question

Sum $\frac{6}{\sqrt{3}},3\sqrt{3},\frac{12}{\sqrt{3}}$, .... to $50$ terms.

Answer 1

$\frac{6}{\sqrt{3}},3\sqrt{3},\frac{12}{\sqrt{3}},...$ to $50$ terms

$⟹$ We can write this series as

$2\sqrt{3},2\sqrt{3},4\sqrt{3},.....$ to $50$ terms

$\therefore a=2\sqrt{3}$

$d=(3\sqrt{3}-2\sqrt{3})=\sqrt{3}$

$\therefore S_n=2a+(n-1)d$

$⟹S_{50}=(2\times 2\sqrt{3})+[(50-1)\times \left(\sqrt{3}\right)]$

$=4\sqrt{3}+49\sqrt{3}$

$S_{50}=53\sqrt{3}$

$⟹S_{50}=86.6025$