Question

Sum $1,\sqrt{3},\mathrm{3......}$ to $12$ terms is

• A. $364(\sqrt{3}+1)$
• B. $364(\sqrt{3}-1)$
• C. $\frac{364}{(\sqrt{3}-1)}$
• D. $\frac{728}{(\sqrt{3}+1)}$

Answer 1

Answer: (A)

$364(\sqrt{3}+1)$

$1,\sqrt{3},3,.....12terms$

It is a G.P with $a=1,r=\sqrt{3}$

$1,\sqrt{3},3,.....12terms$

$S_n=\frac{a\left(r^n-1\right)}{r-1}$

$\Rightarrow S_{12}=\frac{1\left({\left(\sqrt{3}\right)}^{12}-1\right)}{\sqrt{3}-1}$

$\Rightarrow S_{12}=\frac{3^6-1}{\sqrt{3}-1}\times \frac{\sqrt{3}+1}{\sqrt{3}+1}$

$\Rightarrow S_{12}=\frac{728(\sqrt{3}+1)}{3-1}$

$\Rightarrow S_{12}=\frac{728(\sqrt{3}+1)}{2}$

$\Rightarrow S_{12}=364(\sqrt{3}+1)$